Diffusion Parameters Research Articles

Assessing renal interstitial fibrosis using compartmental, non-compartmental, and model-free diffusion MRI approaches

ObjectiveTo assess renal interstitial fibrosis (IF) using diffusion MRI approaches, and explore whether corticomedullary difference (CMD) of diffusion parameters, combination among MRI parameters, or combination with estimated glomerular filtration rate (eGFR) benefit IF evaluation.MethodsForty-two patients with chronic kidney disease were included, undergoing MRI examinations. MRI parameters from apparent diffusion coefficient (ADC), intra-voxel incoherent motion (IVIM), diffusion kurtosis imaging (DKI), and diffusion-relaxation correlated spectrum imaging (DR-CSI) were obtained both for renal cortex and medulla. CMD of these parameters was calculated. Pathological IF scores (1–3) were obtained by biopsy. Patients were divided into mild (IF = 1, n = 23) and moderate-severe fibrosis (IF = 2–3, n = 19) groups. Group comparisons for MRI parameters were performed. Diagnostic performances were assessed by the receiver operator’s curve analysis for discriminating mild from moderate-severe IF patients.ResultsSignificant inter-group differences existed for cortical ADC, IVIM-D, IVIM-f, DKI-MD, DR-CSI VB, and DR-CSI VC. Significant inter-group differences existed in ΔADC, ΔMD, ΔVB, ΔVC, ΔQB, and ΔQC. Among the cortical MRI parameters, VB displayed the highest AUC = 0.849, while ADC, f, and MD also showed AUC > 0.8. After combining cortical value and CMD, the diagnostic performances of the MRI parameters were slightly improved except for IVIM-D. Combining VB with f brings the best performance (AUC = 0.903) among MRI bi-variant models. A combination of cortical VB, ΔADC, and eGFR brought obvious improvement in diagnostic performance (AUC 0.963 vs 0.879, specificity 0.826 vs 0.896, and sensitivity 1.000 vs 0.842) than eGFR alone.ConclusionOur study shows promising results for the assessment of renal IF using diffusion MRI approaches.Critical relevance statementOur study explores the non-invasive assessment of renal IF, an independent and effective predictor of renal outcomes, by comparing and combining diffusion MRI approaches including compartmental, non-compartmental, and model-free approaches.Key PointsSignificant difference exists for diffusion parameters between mild and moderate-severe IF.Generally, cortical parameters show better performance than corresponding CMD.Bi-variant model lifts the diagnostic performance for assessing IF.Graphical

Development of a Fast Running Equivalent Circuit Model with Thermal Predictions for Battery Management Applications

Equivalent circuit modelling (ECM) is a powerful tool to study the dynamic and non-linear characteristics of Li-ion cells and is widely used for the development of the battery management system (BMS) of electric vehicles. The dynamic parameters described by the ECM are used by the BMS to estimate the battery state of charge (SOC), which is crucial for efficient charging/discharging, range calculations, and the overall safe operation of electric vehicles. Typically, the ECM approach represents the dynamic characteristics of the battery in a mathematical form with a limited number of unknown parameters. Then, the parameters are calculated from voltage and current information of the lithium-ion cell obtained from controlled experiments. In the current work, a faster and simplified first-order resistance–capacitance (RC) equivalent circuit model was developed for a commercial cylindrical cell (LGM50 21700). An analytical solution was developed for the equivalent circuit model incorporating SOC and temperature-dependent RC parameters. The solution to the RC circuit model was derived using multiple expressions for different components like open circuit voltage (OCV), instantaneous resistance (R0), and diffusional parameters (R1 and C1) as a function of the SOC and operating temperature. The derived parameters were validated against the virtual HPPC test results of a validated physics-based electrochemical model for the voltage behavior. Using the developed RC circuit model, a polynomial expression is derived to estimate the temperature increase of the cell including both irreversible and reversible heat generation components. The temperature predicted by the proposed RC circuit model at different battery operating temperatures is in good agreement with the values obtained from the validated physics model. The developed method can find applications in (i) onboard energy management by the BMS and (ii) quicker evaluation of cell performance early in the product development cycle.

Connection Failure: Differences in White Matter Microstructure Are Associated with 5-HTTLPR but Not with Risk Seeking for Losses.

S/S carriers of 5-HTTLPR have been found to be more risk seeking for losses compared to L/L carriers. This finding may be the result of reduced top-down control from the frontal cortex due to altered signal pathways involving the amygdala and ventral striatum. The serotonergic system is known to be involved in neurodevelopment and neuroplasticity. Therefore, the aim of this study was to investigate whether structural differences in white matter can explain the differences in risk-seeking behaviour. Lower structural connectivity in S/S compared to L/L carriers and a negative relationship between risk seeking for losses and connectivity were assumed. Diffusion-weighted imaging was used to compute diffusion parameters for the frontostriatal and uncinate tract in 175 genotyped individuals. The results showed no significant relationship between diffusion parameters and risk seeking for losses. Furthermore, we did not find significant differences in diffusion parameters of the S/S vs. L/L group. There were only group differences in the frontostriatal tract showing stronger structural connectivity in the S/L group, which is also reflected in the whole brain approach. Therefore, the data do not support the hypothesis that the association between 5-HTTLPR and risk seeking for losses is related to differences in white matter pathways implicated in decision-making.

Novel Caputo fractional differential approach and hybrid control scheme for finite‐time synchronization of nonidentical delayed reaction–diffusion neural networks

AbstractThis work focuses on the finite‐time synchronization (F‐TS) for nonidentical delayed neural networks (DNNs) including Caputo fractional partial differential operator and reaction–diffusion terms. A novel F‐TS lemma is proposed by constructing a new Caputo differential inequality. Applying the new lemma and designing two hybrid controllers with time delay and the sign function, the F‐TS criteria on the introduced Caputo reaction–diffusion nonidentical DNNs under the Neumann boundary condition are derived by making use of the Filippov differential inclusion, Green's theorem, and fractional Razumikhin theorem. The conditions are expressed through the algebraic inequality which can greatly decrease the computation in checking the F‐TS performance. Moreover, the validity and correctness of the F‐TS results are illustrated by selecting various orders, spatial positions, and diffusion parameters.

Muscle diffusion tensor imaging in facioscapulohumeral muscular dystrophy.

Muscle diffusion tensor imaging has not yet been explored in facioscapulohumeral muscular dystrophy (FSHD). We assessed diffusivity parameters in FSHD subjects compared with healthy controls (HCs), with regard to their ability to precede any fat replacement or edema. Fat fraction (FF), water T2 (wT2), mean, radial, axial diffusivity (MD, RD, AD), and fractional anisotropy (FA) of thigh muscles were calculated in 10 FSHD subjects and 15 HCs. All parameters were compared between FSHD and controls, also exploring their gradient along the main axis of the muscle. Diffusivity parameters were tested in a subgroup analysis as predictors of disease involvement in muscle compartments with different degrees of FF and wT2 and were also correlated with clinical severity scores. We found that MD, RD, and AD were significantly lower in FSHD subjects than in controls, whereas we failed to find a difference for FA. In contrast, we found a significant positive correlation between FF and FA and a negative correlation between MD, RD, and AD and FF. No correlation was found with wT2. In our subgroup analysis we found that muscle compartments with no significant fat replacement or edema (FF < 10% and wT2 < 41 ms) showed a reduced AD and FA compared with controls. Less involved compartments showed different diffusivity parameters than more involved compartments. Our exploratory study was able to demonstrate diffusivity parameter abnormalities even in muscles with no significant fat replacement or edema. Larger cohorts are needed to confirm these preliminary findings.

A computational approach for 2D elliptic singularly perturbed weakly coupled systems of convection–diffusion type with multiple scales and parameters in the diffusion and the convection terms

In this work, we consider the efficient resolution of a 2D elliptic singularly perturbed weakly coupled system of convection–diffusion type, which has small parameters at both the diffusion and the convection terms. We assume that the diffusion parameters can be distinct at each equation of the system, and also, they can have different orders of magnitude, but the convection parameter is the same at both equations of the system. Then, in general, overlapping regular or parabolic boundary layers can appear in the exact solution. The continuous problem is approximated by using the standard upwind finite difference scheme, which is constructed on a special piecewise uniform Shishkin mesh. Then, the numerical scheme is an almost first‐order uniformly convergent method with respect to all the perturbation parameters. Some numerical results, obtained with the numerical algorithm for one test problem, are presented, which show the good performance of the proposed numerical method and also corroborate in practice the theoretical results.

Brain lesion microstructure in neuromyelitis optica spectrum disorder and myelin oligodendrocyte glycoprotein disease.

Neuromyelitis optica spectrum disorder (NMOSD) and myelin oligodendrocyte glycoprotein antibody-associated disease (MOGAD) diagnosis are based on the presence of serological and magnetic resonance imaging (MRI) biomarkers. Diffusion tensor imaging (DTI), neurites orientation dispersion and density imaging (NODDI), and the Spherical Mean Technique (SMT) may be helpful to provide a microstructural characterization of the different types of white matter lesions and give an insight about their different pathological mechanisms. The aim of the study was to characterize microstructural differences between brain typical lesions (TLs) and nontypical lesions (nTLs). A total of 17 NMOSD and MOGAD patients [9 Aquaporin4 (AQP4)+NMO, 2 seronegative-NMO, 6 MOGAD] underwent MRI scans on a 3 Tesla MAGNETON PRISMA. Diffusion parameters (fractional anisotropy; mean diffusivity [MD]; intracellular volume fraction [ICVF]; extra-neurite transverse diffusivity; and extra-neurite MD; neurite signal fraction) were obtained using DTI, NODDI, and SMT. Microstructural parameters within lesions were compared through a generalized linear model using age, sex, and total lesion volume as covariates. In NMOSD/MOGAD whole cohort (total lesions=477), TLs showed increased MD and decreased ICVF compared to nTLs (p<.05), indicating higher inflammation and axonal loss. Similar results were found also in the AQP4+NMO subgroup (decreased ICVF, p<.05). Furthermore, in NMOSD/MOGAD whole cohort and in AQP4+NMO subgroup, TLs showed a trend toward higher EXRATRANS than nTLs, suggesting a more severe degree of demyelination within TLs. TLs and nTLs in NMOSD/MOGAD showed different diffusion MRI-derived microstructural features, with TLs showing a more severe degree of inflammation and fiber disruption with respect to nTLs.

Time-division multiplexing (TDM) sequence removes bias in T2 estimation and relaxation-diffusion measurements.

To compare the performance of multi-echo (ME) and time-division multiplexing (TDM) sequences for accelerated relaxation-diffusion MRI (rdMRI) acquisition and to examine their reliability in estimating accurate rdMRI microstructure measures. The ME, TDM, and the reference single-echo (SE) sequences with six echo times (TE) were implemented using Pulseq with single-band (SB-) and multi-band 2 (MB2-) acceleration factors. On a diffusion phantom, the image intensities of the three sequences were compared, and the differences were quantified using the normalized root mean squared error (NRMSE). For the in-vivo brain scan, besides the image intensity comparison and T2-estimates, different methods were used to assess sequence-related effects on microstructure estimation, including the relaxation diffusion imaging moment (REDIM) and the maximum-entropy relaxation diffusion distribution (MaxEnt-RDD). TDM performance was similar to the gold standard SE acquisition, whereas ME showed greater biases (3-4× larger NRMSEs for phantom, 2× for in-vivo). T2 values obtained from TDM closely matched SE, whereas ME sequences underestimated the T2 relaxation time. TDM provided similar diffusion and relaxation parameters as SE using REDIM, whereas SB-ME exhibited a 60% larger bias in the <R2> map and on average 3.5× larger bias in the covariance between relaxation-diffusion coefficients. Our analysis demonstrates that TDM provides a more accurate estimation of relaxation-diffusion measurements while accelerating the acquisitions by a factor of 2 to 3.

Agent-based model demonstrates the impact of nonlinear, complex interactions between cytokinces on muscle regeneration.

Muscle regeneration is a complex process due to dynamic and multiscale biochemical and cellular interactions, making it difficult to identify microenvironmental conditions that are beneficial to muscle recovery from injury using experimental approaches alone. To understand the degree to which individual cellular behaviors impact endogenous mechanisms of muscle recovery, we developed an agent-based model (ABM) using the Cellular-Potts framework to simulate the dynamic microenvironment of a cross-section of murine skeletal muscle tissue. We referenced more than 100 published studies to define over 100 parameters and rules that dictate the behavior of muscle fibers, satellite stem cells (SSCs), fibroblasts, neutrophils, macrophages, microvessels, and lymphatic vessels, as well as their interactions with each other and the microenvironment. We utilized parameter density estimation to calibrate the model to temporal biological datasets describing cross-sectional area (CSA) recovery, SSC, and fibroblast cell counts at multiple timepoints following injury. The calibrated model was validated by comparison of other model outputs (macrophage, neutrophil, and capillaries counts) to experimental observations. Predictions for eight model perturbations that varied cell or cytokine input conditions were compared to published experimental studies to validate model predictive capabilities. We used Latin hypercube sampling and partial rank correlation coefficient to identify in silico perturbations of cytokine diffusion coefficients and decay rates to enhance CSA recovery. This analysis suggests that combined alterations of specific cytokine decay and diffusion parameters result in greater fibroblast and SSC proliferation compared to individual perturbations with a 13% increase in CSA recovery compared to unaltered regeneration at 28 days. These results enable guided development of therapeutic strategies that similarly alter muscle physiology (i.e. converting extracellular matrix [ECM]-bound cytokines into freely diffusible forms as studied in cancer therapeutics or delivery of exogenous cytokines) during regeneration to enhance muscle recovery after injury.

Agent-based model demonstrates the impact of nonlinear, complex interactions between cytokines on muscle regeneration

Muscle regeneration is a complex process due to dynamic and multiscale biochemical and cellular interactions, making it difficult to identify microenvironmental conditions that are beneficial to muscle recovery from injury using experimental approaches alone. To understand the degree to which individual cellular behaviors impact endogenous mechanisms of muscle recovery, we developed an agent-based model (ABM) using the Cellular-Potts framework to simulate the dynamic microenvironment of a cross-section of murine skeletal muscle tissue. We referenced more than 100 published studies to define over 100 parameters and rules that dictate the behavior of muscle fibers, satellite stem cells (SSCs), fibroblasts, neutrophils, macrophages, microvessels, and lymphatic vessels, as well as their interactions with each other and the microenvironment. We utilized parameter density estimation to calibrate the model to temporal biological datasets describing cross-sectional area (CSA) recovery, SSC, and fibroblast cell counts at multiple timepoints following injury. The calibrated model was validated by comparison of other model outputs (macrophage, neutrophil, and capillaries counts) to experimental observations. Predictions for eight model perturbations that varied cell or cytokine input conditions were compared to published experimental studies to validate model predictive capabilities. We used Latin hypercube sampling and partial rank correlation coefficient to identify in silico perturbations of cytokine diffusion coefficients and decay rates to enhance CSA recovery. This analysis suggests that combined alterations of specific cytokine decay and diffusion parameters result in greater fibroblast and SSC proliferation compared to individual perturbations with a 13% increase in CSA recovery compared to unaltered regeneration at 28 days. These results enable guided development of therapeutic strategies that similarly alter muscle physiology (i.e. converting extracellular matrix [ECM]-bound cytokines into freely diffusible forms as studied in cancer therapeutics or delivery of exogenous cytokines) during regeneration to enhance muscle recovery after injury.

Extending a Multiphysics Li-Ion Battery Model from Normal Operation to Short Circuit and Venting

Mitigation of Li-ion battery system fires consists of reliable fault detection and proactive, fast discharge control. Both require modeling of failure modes due to high temperatures and currents between normal operation and thermal runaway. In this work, we present a control-oriented, reduced-order, multiphysics model that captures the electrochemical, thermal, gas generation, mechanical expansion, and venting behavior of NMC pouch cells undergoing an external short circuit (ESC) from different initial state-of-charge (SOC). The model is parameterized through experiments by fitting the solid-electrolyte interphase (SEI) decomposition rate, the cell’s thermal parameters, and the particle solid-phase diffusion parameters to capture the first venting timing, peak temperature, and diffusion-limited electrical behavior at high currents. Using a single parameter set, the multiphysics model can capture behavior during an ESC to predict whether a cell will generate gas and vent, predict the vent timing within 10 seconds of it occurring in the experiment, and maximum cell expansion pressure within 10 kPa for cells that did not vent. The model can also predict the SOC trajectory for cells with a high initial SOC within 6% SOC for the 15-minute discharge or until the cell vents.

Age-related T1 mapping, fat fraction, diffusion and perfusion parameters of the lumbar vertebrae in healthy children under 3.0 T MRI

Compare the T1 mapping, fat fraction, diffusion and perfusion parameters of the lumbar vertebrae of different age groups to establish normal values for healthy children and observe the trends in these parameters with age. A total of 146 healthy children (0-14 years) were included in this prospective study and underwent 3.0 T lumbar MRI examination. The study cohort was divided into five age groups (Group A∼E) according to development milestones in children. T1 mapping, Dixon and IVIM (intravoxel incoherent motion)sequence images were used to measure the parameters of lumbar vertebrae 2-4. The normal values of each parameter were measured and compared across different age groups. The T1 value was negatively correlated with age (r=-0.619, p<0.001). The fat fraction (FF%) was positively correlated with age (r=0.635, p<0.001). There was a negative correlation between the D value and age (r=-0.406, p<0.001). The D∗ value was positively correlated with age (r=0.54, p<0.001). The f value was positively correlated with age (r=0.775, p<0.001). The inflexion points of the T1 value and FF% curves were at approximately 3 years old (36 months).The inflexion points of the IVIM-related parameter curves were approximately 5 years old (60 months). The age-dependent differences in the vertebral body parameters of this pediatric cohort suggest changes in the bone marrow composition and cellular structure of the vertebral body during physiological growth in children. The establishment of normal values of children's lumbar spine can facilitate the clinical study of diseases.

Diffusion properties of Gabonese tropical hardwoods and European softwoods measured with low-tech equipment and by an inverse method

This paper presents an experimental approach to studies of the sorption and diffusion properties of wood. Five timber species - three African tropical hardwoods, Padauk, Okoume and Iroko, and two temperate softwoods, Silver fir and Douglas fir - were studied in adsorption mode. Specimens with 10- and 20-mm longitudinal (L) and transverse (RT) thickness were waterproofed on their sides to force diffusion in those directions. After kiln drying the specimens were hung with nylon wires under cover in a home-made box in which salt solutions provided constant relative humidity (RH), and conditioned at 43, 55, 75, 84 and 97% RH in successive steps. Temperature was maintained between 20 and 24°C. During the equilibration steps the samples were periodically weighed without altering the environmental conditions imposed, by hanging the nylon wire to a spring gauge through a small hole in the box cover. The sorption isotherm properties and diffusion parameters were obtained using an inverse method based on optimization of a 1D finite difference model. The parameters obtained show a decreasing correlation between diffusion coefficient and density, as observed by several authors in the literature. They also illustrate the impact of extractives on the sorption isotherm parameters. These results show that tropical species with high density or many extractives behave very differently to European softwoods, which impedes the application of Eurocode 5 equilibrium standards for these species.

Importance of Cosmic-Ray Propagation on Sub-GeV Dark Matter Constraints

We study sub-GeV dark matter (DM) particles that may annihilate or decay into Standard Model particles producing an exotic injection component in the Milky Way that leaves an imprint in both photon and cosmic-ray (CR) fluxes. Specifically, the DM particles may annihilate or decay into e + e −, μ + μ −, or π + π − and may radiate photons through their e ± products. The resulting e ± products can be directly observed in probes such as Voyager 1. Alternatively, the e ± products may produce bremsstrahlung radiation and upscatter the low-energy Galactic photon fields via the inverse Compton process, generating a broad emission from X-ray to γ-ray energies observable in experiments such as XMM-Newton. We find that we get a significant improvement in the DM annihilation and decay constraints from XMM-Newton (excluding thermally averaged cross sections of 10−31 cm3 s−1 ≲ 〈σ v〉 ≲ 10−26 cm3 s−1 and decay lifetimes of 1026 s ≲ τ ≲ 1028 s, respectively) by including best-fit CR propagation and diffusion parameters. This yields the strongest astrophysical constraints for this mass range of DM of 1 MeV to a few GeV and even surpasses cosmological bounds across a wide range of masses as well.

Properties of tape cast (Na, K, Li) (Nb, Sb, Ta)O3 -based ceramics sintered in reduced atmosphere and its application in triaxial piezoelectric accelerometer

In this study, we utilized the tape-casting method to produce Pb-free (Na0·52K0·4425Li0.0375) (Nb0·8925Sb0·07Ta0.0375)O3 + 2 mol% MnCO3 + y mol% LiF (y = 0 to 3) piezoelectric ceramics. We investigated the impact of LiF sintering in a reduced atmosphere on microstructure, dielectric properties, impedance spectroscopy, and piezoelectric performance. By analyzing the degree of diffuse phase transition, we observed increased density and enhanced long-range order in the sample doped with 1 mol% LiF, which exhibited optimal piezoelectric properties (d33 = 265 pC/N and kp = 0.437) and a minimal diffusion parameter. Moreover, LiF doping enabled sintering at 1020 °C under low PO2, facilitating potential co-firing with Cu inner electrodes to further enhance the piezoelectric performance. Using the optimized parameters, we fabricated a cross-type triaxial piezoelectric accelerometer, demonstrating sensitivities of 2.33, 2.44, and 10.6 mV/g along the X, Y, and Z axes, respectively, with a resonance frequency of ∼2600 Hz and frequency range of ∼1300 Hz. This accelerometer holds promise for vibration measurements in low-frequency mechanical systems.

Experimental and numerical study on moisture diffusion behavior of 3D woven composite

In this paper, a meso-scale finite element model was established to investigate the moisture diffusion in 3D woven carbon fiber reinforced composites (CFRCs), and to analyze the internal stresses caused by hygroscopic deformation. To quickly obtain the mesoscopic moisture diffusion parameters, an optimization procedure that fitted the simulation results to the experimental results was implemented to achieve automatic inverse identification of each parameter. The homogenized analytical models for describing the moisture diffusion in yarns and resin, specifically Fick’s and Langmuir-type models, were evaluated. The results indicated that Langmuir-type model provided more accurate fitting results, attributed to its consideration of anomalous moisture absorption. Furthermore, the internal stress induced by moisture absorption was analyzed for composites aging at 82 °C over different time intervals. The accumulation of hygroscopic stress was observed at the intersection of warp and weft yarns, as well as at the interface between the weft yarn and matrix.

A chance-constrained net revenue model for online dynamic predictive maintenance decision-making

Most models for predictive maintenance (PdM) decision-making focus on the expected value of a system performance metric (e.g., the expected cost rate). However, focusing solely on such expected values may overlook the significant risks of resulting PdM decisions. Indeed, it would be practically valuable to make the optimal PdM decision by considering the least probability of achieving a target system performance. Furthermore, emphasizing only maintenance costs without accounting for operational revenues can render the maintenance strategies unappealing, particularly when the revenues across system lifecycles are significant. This study introduces a method that employs a stochastic net revenue model and chance-constrained programming to address these issues in PdM decision-making, wherein the preventive maintenance cost is proportional to the system's current degradation state. By exemplifying system degradation with the Gamma process, we derive the probability density function of stochastic net revenue and present a Bayesian method to simultaneously update the drift and diffusion parameters of the Gamma process model. The effectiveness and practical applicability of our proposed chance-constrained net revenue model and parameter updating method are demonstrated through a numerical example and a case study.

Study on the Diffusion Parameters of Newtonian Fluid in High-Pressure Jet Disturbance Grouting

In order to investigate the diffusion mechanism of slurry in post-pile grouting, this study develops a formula for calculating the diameter and the climb height of the cement core of jet grouting (CCJG). This research conducts field orthogonal tests using a self-developed grouting nozzle to analyze the effects of disturbance pressure (DP), disturbance time (DT), grouting pressure (GP), and the water–cement ratio (W/C) on the dimensions and strength of the CCJG. The findings revealed that the theoretical formula for calculating the diameter of the CCJG deviates by approximately 8% from the field test results, confirming the formula’s validity. In addition, the DP and DT significantly influence the volume of the CCJG, displaying a linear increase with their augmentation. Conversely, the W/C and DP predominantly affect the CCJG’s strength. Notably, an increase in the W/C results in diminished strength, whereas an increase in the DP enhances it. In addition, soil reinforcement is achieved through replacement, mixing, and compaction as the grout flows outward from the center of the grouting hole. These insights offer a theoretical foundation and technical support for effective grouting construction practices.

Histogram analysis of intravoxel incoherent motion imaging: Correlation with molecular prognostic factors and combined subtypes of breast cancer

PurposeTo look for links between diffusion and IVIM parameters and different molecular subtypes and prognostic factors through histogram analysis. Materials and methodsA total of 139 patients with breast cancer who had pre-operative MRI examinations were enrolled in this retrospective study. Histograms of the diffusion and IVIM parameters were analyzed for the whole tumor, and an association was investigated between the parameters and the different molecular prognostic factors and subtypes using the nonparametric test, Spearman's rank correlation, and receiver operating characteristic (ROC) curve. ResultsThe histogram metrics of the diffusion and IVIM parameters were significantly different for molecular prognostic factors such as human epidermal receptor factor-2 (HER2), progesterone receptor, estrogen receptor, and ki-67. All histogram metrics displayed a poor correlation with all groups (r = −0.28-0.29). There were significant differences in the histogram metrics for the Luminal B-HER2 (−) vs. HER2-positive (non-luminal) subtypes in the mean and 10th percentile D, with the area under the curves (AUCs) of 0.742 and 0.700, respectively, and for the Luminal A and HER2-positive (non-luminal) subtypes in the 90th percentile and entropy of D*, with AUCs of 0.769 and 0.727, respectively. ConclusionThe histogram metrics of IVIM parameters exhibited links with breast cancer prognosis factors and combined subtypes.

High-order Lagrange-Galerkin methods for the conservative formulation of the advection-diffusion equation

Abstract We introduce in this paper the numerical analysis of high order both in time and space Lagrange-Galerkin methods for the conservative formulation of the advection-diffusion equation. As time discretization scheme we consider the Backward Differentiation Formulas up to order $q=5$. The development and analysis of the methods are performed in the framework of time evolving finite elements presented in C. M. Elliot and T. Ranner, IMA Journal of Numerical Analysis41, 1696–1845 (2021). The error estimates show through their dependence on the parameters of the equation the existence of different regimes in the behavior of the numerical solution; namely, in the diffusive regime, that is, when the diffusion parameter $\mu $ is large, the error is $O(h^{k+1}+\varDelta t^{q})$, whereas in the advective regime, $\mu \ll 1$, the convergence is $O(\min (h^{k},\frac{h^{k+1} }{\varDelta t})+\varDelta t^{q})$. It is worth remarking that the error constant does not have exponential $\mu ^{-1}$ dependence.