Diffusion Coefficients Of Components Research Articles

Relation of acrylic acid polymerization behavior in deep eutectic solvent to water content: Computer simulation and experiment

Polymerizable deep eutectic solvents (DES) are promising starting materials for preparation of eutectogels and hydrogels that can be applied in drug delivery, as strain sensors and various components of soft electronics. However, the understanding of relationship between the molecular structure, physicochemical properties and polymerization behavior of such systems in pure state and in their mixtures with water is not well studied yet. In this work we report the results of both computer simulation and experimental investigations for polymerizable choline chloride/acrylic acid DES and its mixtures with water. Molecular dynamics was applied to reveal the influence of water on the structure of polymerizable DES at the molecular and supramolecular levels. The diffusion coefficients of DES components with different water content were measured using NMR. The course of photoinduced polymerization of DES/water mixtures was traced using FTIR spectroscopy, while the molar mass and hydrodynamic characteristics of obtained polyacrylic acid were studied by means of static and dynamic light scattering. It was found that addition of water leads to a gradual decrease in size of the acrylic acid clusters that exist in pure DES and is accompanied by an increase in orientation mobility and diffusion coefficients of components. The maximal molar mass was obtained for the polymer prepared by polymerization of DES with 5 wt% of water. This can be attributed to the optimal combination of acrylic acid clusters size and increased mobility of components.

Strong convergence of multi-scale stochastic differential equations with a full dependence

This paper considers the strong convergence of multi-scale stochastic differential equations, where diffusion coefficient of the slow component depends on fast process. In this situation, it is well-known that strong convergence in the averaging principle does not hold in general.We propose a new approximation equation, and prove that the order of strong convergence is 1/2 via the technique of Poisson equation. In particular, when diffusion coefficient of the slow component does not depend on fast process, the approximation equation is exactly the averaged equation. This provides us a new perspective to study the strong convergence of multi-scale stochastic differential equations with a full dependence.

Analysis of the self-healing mechanism of TB compound-modified asphalt based on molecular dynamics

To investigate the intrinsic self-healing behavior of terminal blend (TB)-modified asphalt (TBMA), this study establishes four models of matrix asphalt, TBMA, TBMA containing styrene-butadiene-styrene (TB_SBS), and TBMA containing ethylene vinyl acetate (TB_EVA) based on molecular dynamics, and the self-healing ability of the four types of asphalt was evaluated by means of the diffusion coefficient, diffusion activation energy, and pre-exponential factor. Finally, the study analyzes and validates the self-healing performance of the asphalt through fatigue shear-healing tests. The results showed that the self-healing potentials of the four types of asphalt, as determined by the diffusion coefficient, diffusion activation energy, and pre-exponential factor, were (in descending order) TB_SBS, TBMA, TB_EVA, and matrix asphalt. In addition, the diffusion coefficient of the TBMA was increased relative to the matrix asphalt, SBS polymer further increased the diffusion coefficient, and EVA modifier had an inhibitory effect, which was related to the viscoelasticity and mechanical performance of the material. Besides, the diffusion coefficient enhancement effect of the SBS modifier on the TBMA was greater than the inhibition effect, which mainly derived from the enhancement of the diffusion coefficient of lightweight components in significantly enhancing the self-healing ability the TBMA. From microscopic and macroscopic scales, the shear-fatigue healing tests showed excellent correlation with the simulation results, demonstrating that molecular dynamics can be used to model the self-healing process of asphalt.

CT and MRI findings of small cell neuroendocrine carcinoma of the urinary bladder: comparison with urothelial carcinoma

ObjectiveThis study aimed to evaluate the efficacy of CT and MRI findings to differentiate small cell neuroendocrine carcinoma (SCNEC) from urothelial carcinoma (UC) of the urinary bladder.Materials and methodsThis study included 90 patients with histopathologically confirmed bladder cancer (10 SCNECs and 80 UCs). Eight patients with bladder SCNEC and 80 with UC underwent CT and MRI, whereas the remaining two patients with SCNEC underwent CT alone before treatment. CT and MRI findings were retrospectively evaluated and compared between the two pathologies.ResultsThe maximum diameter (36.5 mm vs. 19.0 mm, p < 0.01) and height (22.0 mm vs. 14.0 mm, p < 0.01) of the tumor in bladder SCNEC were higher than in UC. The pedunculated configuration (20% vs. 61%, p < 0.05) and irregular tumor margins (20% vs. 76%, p < 0.01) in bladder SCNEC were less common than in UC. The CT attenuation of the solid component in unenhanced CT images was higher in bladder SCNEC than in UC (37 Hounsfield unit [HU] vs. 34 HU, p < 0.01). The apparent diffusion coefficient (ADC) of the solid component in bladder SCNEC was lower than in UC (0.49 × 10−3 mm2/s vs. 1.02 × 10−3 mm2/s, p < 0.01).ConclusionIn comparison with UC, bladder SCNEC was larger, had higher unenhanced CT attenuation, and had a lower ADC value. The pedunculated configuration and irregular tumor margins were typical of bladder UC.Graphical abstract

КОЭФФИЦИЕНТЫ ДИФФУЗИИ И АКТИВНОСТЬ КОМПОНЕНТОВ ВОДНОСПИРТОВЫХ СМЕСЕЙ В ПОЛИУРЕТАНОВЫХ ПЛЕНКАХ НА ОСНОВЕ АМИНОЭФИРОВ БОРНОЙ И ОРТОФОСФОРНОЙ КИСЛОТ

The work carried out studies to determine the diffusion coefficients and activities of water, isopropyl and ethyl alcohols in polymer polyurethane films based on amino esters of boric and orthophosphoric acids at temperatures of 22, 40 and 60 °C. To determine the diffusion coefficients, we used data on the dynamics of sorption of low molecular weight components in the polymers under study, presented in our previous study. To describe the process of swelling of a polymer film, the Fick differential equation was used; the process was represented as unsteady diffusion in a flat plate. The initial condition was the absence of a component in the polymer at the initial moment of time; the solution to the differential equation was the non-stationary field of concentrations of the component in the film. The experimental dependences of changes in the volume-mass concentration of components in the polymer were described using the Heaviside switching function; due to the presence of a maximum in the swelling curve, it is associated with a restructuring of the polymer structure that occurs due to possible relaxation processes. By minimizing the discrepancies between the calculated and experimental values of the concentration versus time dependence, the diffusion coefficients of pure components in AEPA and AEBA films were determined. Based on data on the diffusion of components through polymer films, the separation characteristics of polymers were assessed for their use as a selective layer of pervaporation membranes. Based on swelling data over long periods of time for water-alcohol mixtures of various compositions, the parameters of the Flory-Huggins model were determined for calculating the activities of components in the polymer. It was shown that among the solvents under study, water has the highest diffusion coefficient, and isopropyl alcohol has the lowest, regardless of the type of film (AEPA/AEBA). For all films, there is a tendency for the diffusion coefficient to increase with increasing temperature, regardless of the solvent.

A kinetic model of diffusional phase transformations in ternary line compounds and determination of diffusion coefficients: Application to the Nb–Mo–Si system

The diffusional phase transformations in inhomogeneous multicomponent systems play an important role in affecting the material properties. Ternary line compounds, which are ternary phases with components that have both large and small solid solubility, are often observed in applications. They are different from solid solutions with variable composition ratios and stoichiometric compounds with fixed composition ratios. However, the existing models cannot quantitatively characterize the diffusional phase transformations in ternary line compounds. Therefore, by introducing the state equation related to the chemical potential and mole fraction, a kinetic model of diffusional phase transformations was established for the first time to describe the mole fraction evolution and phase growth in ternary line compounds. Furthermore, a method to determine the tracer diffusion coefficients of components related to the mole fraction and crystal phase structure in ternary line compounds was proposed, and applied to the diffusion of Nb-Mo-Si ternary system composed of the MoSi2 and Nb. During the high-temperature diffusion process of Nb-MoSi2, the silicide-poor phase (Mo, Nb)5Si3 is formed, which is a typical ternary line compound. Based on the diffusion experiments and inverse calculations, the tracer diffusion coefficients of components in ternary line compound (Mo, Nb)5Si3 were experimentally obtained. Moreover, ab-initio calculations of defect energetics clarified the microscopic diffusion mechanisms in the silicide-poor phase, and explained the reason why that the diffusion coefficient of Si decreases significantly with the increase of Nb mole fraction in ternary line compound (Mo, Nb)5Si3. The research provides valuable guidance for modeling and analyzing the diffusional phase transformation of multi-component systems.

An Experimental Approach to Determining the Average Diffusion Coefficient of Volatile Components in Polymer Waste Materials

One of the major challenges in recycling plastics is the removal of undesired volatile components from the polymeric phase, which may reduce process efficiency and negatively affect product quality. Accordingly, the recycling industry employs a broad range of degassing techniques, the efficiency of which often depends on the diffusion coefficient—a measure of the mass transport of volatile components in polymeric phases. The aim of this study was to develop a practically feasible experimental approach using thermogravimetric analysis (TGA) to determine the average diffusion coefficient of volatile components in polymer waste materials. First, the TGA method was validated with a pressure decay apparatus (PDA) using predefined binary material mixtures: Thin sheets were pressed from virgin high-density polyethylene (HDPE) and polypropylene (PP) and deliberately saturated with toluene in a sorption experiment. These saturated samples were then used in TGA and PDA desorption experiments at 60 °C, 80 °C and 100 °C, which yielded similar results with an average difference of 7.4% for the HDPE-toluene system and 14.7% for the PP-toluene system. When validated, TGA was employed to determine the diffusion coefficient of volatile components in post-industrial plastic waste melt at a temperature of 220 °C. The proposed method contributes to the understanding of diffusion-based mass transport in polymer waste materials and provides a key parameter for model-based process control and optimization. In practice, the diffusion coefficient results can be used to predict the degassing performance of an extrusion process in the mechanical recycling of plastic waste.

Study on the mechanism of bond strength generation and debonding failure between basalt fiber and asphalt based on molecular dynamics

Asphalt-basalt fiber interface models were established based on molecular dynamics to explore the microscopic bond characteristics between basalt fiber and asphalt. The debonding failure behavior between basalt fiber and asphalt was examined by comparing its bond strength and the asphalt diffusion coefficient. The effects of temperature and basalt fiber oxide on these variables were also examined. The findings demonstrate that the order of diffusion coefficients of the asphalt components on the surface of basalt fiber is as follows: saturate > aromatic > resin > asphaltene, where the diffusion activation energy of the saturate is the largest and more sensitive to temperature, while the diffusion of resin and asphaltene is less influenced by temperature. The interfacial energy between the four oxides of basalt fiber and asphalt is CaO > MgO > Al2O3 > SiO2 in descending order. As the temperature increases, the interaction force between internal molecules of asphalt becomes smaller, and repulsive forces appear between the asphalt interfaces when the temperature of asphalt is heated to 438 K. In the microscopic particle state, the basalt fiber reinforced asphalt is more prone to debonding failure within the asphalt, while the adhesion property of the basalt fiber and asphalt interface is relatively stable. The study's findings can serve as an experimental foundation for the inclusion of basalt fibers in asphalt mixtures.

Adsorption layer of complex oil components in organic-rich shale: A molecular dynamics simulation study

Shale oil is enriched in organic-rich shale, and its reservoir is mainly composed of micro-nano pore throats. The fluid adsorption layer in nano-confined channels complicates the fluid properties and transport patterns. In this study, equilibrium molecular dynamics was used to study the distribution states and diffusion patterns of complex oil components in organic matter represented by kerogen and four inorganic minerals represented by illite, quartz, calcite, and albite. The thickness and proportion of adsorption layers with different pores are quantitatively calculated. The adsorption capacity is in the following order: kerogen > illite > albite > calcite > quartz. According to the interaction energy, the adsorption stability of oil on surfaces with different pores is in the following order: illite > albite > calcite > kerogen > quartz, and the main forces of adsorption with different pores are obtained. With the increase in pore size, the proportion of light components in the adsorption layer increases, and the proportion of heavy components decreases. The oil components in quartz, calcite, and albite gradually desorb with the increase of pore size, while the oil components in illite are the opposite. The adsorption proportion of other components except for toluene in the kerogen pore increased. The diffusion rate of components in kerogen, quartz, and calcite is related to their relative atomic mass. The diffusion coefficient of components in illite is related to the polarity of components. The diffusion rate of components in small pore sizes of albite minerals is related to the polarity of components, and the diffusion rate of components in large pore sizes is related to the relative atomic mass of components. The effect of temperature and initial moisture content on pores is related to the type of pores.

Modeling contractility kit-mediated cytoskeletal network assembly.

The proper function of the cytoskeleton enables mechanoresponsiveness, the ability of cells to sense and respond to mechanical cues. Myosin II, cortexillin I and IQGAP proteins preassemble in the cytoplasm of Dictyostelium cells into contractility kits (CKs). These CKs are thought to play a pivotal role in the regulation and delivery of contractile proteins to sites of mechanical stress. The IQGAPs complementarily regulate the mechanoresponsiveness of cortexillin I-myosin II elements within CKs. Whereas cells that have only IQGAP2 are highly mechanoresponsive, those that have only IQGAP1 are not. Moreover, double mutants lacking both IQGAPs are also mechanoresponsive, suggesting that IQGAP1 serves as an inhibitor of cortexillin I and myosin II, and part of the role of IQGAP2 is to alleviate IQGAP1's inhibition. To investigate the mechanism of CK self-assembly and the possible molecular means for IQGAP regulation, we developed in SpringSaLaD a coarse-grained excluded-volume molecular model in which all protein polymers are represented by nm-sized spheres connected by spring-like links. The model is parameterized using experimentally measured values acquired through fluorescence cross-correlation spectroscopy (FCCS) and fluorescence correlation spectroscopy (FCS), which describe the interaction affinities and diffusion coefficients for individual molecular components. Simulations of the model provided cluster diffusion coefficients, distributions of cluster sizes, cluster component distributions, and IQGAP ratios in the clusters. Simulations of wild-type and null-mutant conditions revealed that the temporal order of assembly of these kits is dominated by myosin II dimer formation and that IQGAP proteins mediate cluster growth. Additionally, our simulations predicted, and FCCS experiments confirmed, the existence of CKs that incorporate both IQGAP1 and IQGAP2. This molecular model serves to describe the formation of CKs and how their assembly enables and regulates mechanoresponsiveness.

Correlating electrochemical biochar oxidation with electrolytes during biochar-assisted water electrolysis for hydrogen production

Biochar-assisted water electrolysis (BAWE) for hydrogen production is employed to reduce energy consumption by replacing the oxygen evolution reaction (OER) with thermodynamically more favorable biochar oxidation reaction (BOR). Electrolyte, as a carrier to dissolve the biochar particles and form conductive solution, is essential for the transfer and transformation of biochar particles and free radical precursors. Herein, the effects of electrolyte type, concentration, and pH on the BOR performance of BAWE system were investigated. Results show that 1 M KOH solution as an electrolyte was more suitable for the BAWE system, and the BOR of the alkaline BAWE system had the higher electrochemical activity (E10 = 1.649 V vs RHE, 56 mV∙dec−1) compared with the OER in conventional water electrolysis system (E10 = 1.982 V vs RHE, 189 mV∙dec−1). The anion adsorption phenomenon appeared in acidic media restricted the BOR kinetics. In addition, the diffusion coefficient of anodic reaction components showed a first decrease and then increase trend when the pH increased. And the diffusion coefficient reached the maximum value of 3.11 × 10−3 cm2∙s−1 at pH of 13.98, which was favorable for accelerating the diffusion of reaction components from the bulk solution to the electrode surface. This work can provide guidance for further improving the diffusion of reaction components, the biochar oxidation rate and hydrogen production in BAWE process.

Particle-based model of mechanosensory contractility kit assembly

Cell shape change processes, such as proliferation, polarization, migration, and cancer metastasis, rely on a dynamic network of macromolecules. The proper function of this network enables mechanosensation, the ability of cells to sense and respond to mechanical cues. Myosin II and cortexillin I, critical elements of the cellular mechanosensory machinery, preassemble in the cytoplasm of Dictyostelium cells into complexes that we have termed contractility kits (CKs). Two IQGAP proteins then differentially regulate the mechanoresponsiveness of the cortexillin I-myosin II elements within CKs. To investigate the mechanism of CK self-assembly and gain insight into possible molecular means for IQGAP regulation, we developed a coarse-grained excluded volume molecular model in which all protein polymers are represented by nm-sized spheres connected by spring-like links. The model is parameterized using experimentally measured parameters acquired through fluorescence cross-correlation spectroscopy and fluorescence correlation spectroscopy, which describe the interaction affinities and diffusion coefficients for individual molecular components, and which have also been validated via several orthogonal methods. Simulations of wild-type and null-mutant conditions implied that the temporal order of assembly of these kits is dominated by myosin II dimer formation and that IQGAP proteins mediate cluster growth. In addition, our simulations predicted the existence of “ambiguous” CKs that incorporate both classes of IQGAPs, and we confirmed this experimentally using fluorescence cross-correlation spectroscopy. The model serves to describe the formation of the CKs and how their assembly enables and regulates mechanosensation at the molecular level.

NMR studies of Sugammadex formulations complexes with steroidal neuromuscular blockers drugs Rocuronium and Vecuronium

Sugammadex a modified γ-cyclodextrin forms strong water-soluble complexes with steroid neuromuscular blockers (NMBs) such as Rocuronium and Vecuronium, creating a concentration gradient that favors the displacement of these drugs from the neuromuscular junction to the plasma, quickly reversing the neuromuscular obstruction. This work described the comparative evaluation between two formulations of Sugammadex solution from Blau Farmacêutica S/A compared to reference formulation Bridion®, by Nuclear Magnetic Resonance (NMR) 1H and DOSY techniques. The formulations were evaluated in presence of Rocuronium and Vecuronium in the stoichiometric proportions of 1:1 and 1:0.4 for both NMBs. NMR 1H spectra of the formulations Blau and Bridion® did not show significant variations of chemical shifts showing similar physicochemical parameters. Chemical shifts and diffusion coefficients of NMBs were influenced by the presence of Sugammadex when compared to NMBs formulations in the absence of any cyclodextrin, directly demonstrating the strong intermolecular interaction associated with the host molecule in a high proportion. No significant variation in the diffusion coefficients of the key components between formulations in the presence of NMBs in the equimolar 1:1 and 1:04 w/w ratios was observed. The constants Ka and KD were determined and presented 16.7 and 0.06 mM values respectively, according to literature for this system.

Quantification of preferential and mutual mass transfer of gases-light oil systems at high pressures and elevated temperatures by dynamic volume analysis

• Dynamic liquid volume due to gas dissolution and light-component extraction is measured and recorded continuously. • Gas fractions at the beginning and end of each test is respectively measured with GC. • Light-component extraction from oil phase to gas phase results in a shrinkage of the oil phase with pressure. • Both individual diffusion coefficients for each gas component of a gas mixture in the oil phase and oil components extracted from oil phase to gas phase are increased with pressure. • By isolating natural convection from the molecular diffusion, larger diffusivities are determined. In this study, a robust and pragmatic technique has been developed for the first time to quantify preferential and mutual mass transfer of gases-light oil systems at high pressures and elevated temperatures by performing dynamic volume analysis. Experimentally, diffusion tests have been conducted for gases-light oil systems at high pressures and a constant reservoir temperature with a PVT setup. During experiments, the dynamic liquid volume due to gas dissolution and light-component extraction has been measured and recorded continuously, while gas fractions at the beginning and end of each test have been measured with gas chromatography (GC) analysis, respectively. Theoretically, the preferential and mutual diffusion between gas and oil phases can be quantified by minimizing the discrepancies between the measured and calculated swelling factor and gas composition. According to the measured swelling factors, oil swelling effect slows down during the late stage of a diffusion experiment, indicating that CO 2 dissolution is transited from the natural convection-dominated period to the diffusion-dominated period. Compared to the swelling effect at a higher pressure, the effect of light-component extraction on the determined diffusion coefficients of gas components becomes weaker. In addition, both individual diffusion coefficients for each gas component of a gas mixture in an oil phase and oil component extracted from the oil phase to the gas phase are increased with pressure. The diffusion-convection model allows us to isolate the natural convection from the molecular diffusion, leading to larger diffusivities compared with the ones determined from the conventional method.

Analysis of the Self-Healing Process of Asphalt and its Influencing Factors

Molecular dynamics was used in this study to understand the self-healing behavior and mechanism of asphalt. Density, solubility, and mean square displacement parameters were analyzed to confirm the validity of the matrix asphalt model. Molecular simulation software was used to develop a microscopic matrix asphalt self-healing model at the nanoscale. Cracking width of asphalt microcracks was represented by setting different vacuum layer thicknesses as the asphalt self-healing model. Density and diffusion coefficient of the self-healing model were obtained by running the molecular software to understand the entire process of asphalt healing. The self-healing mechanism of the matrix asphalt was analyzed. Results showed that the entire self-healing process of asphalt could be clearly divided into four stages, namely, external environment energy endowment, model end healing, asphalt microcrack healing, and self-healing model self-diffusion stages. Molecules of each component in the asphalt self-healing process diffuse and move mutually under constant temperature conditions. The diffusion coefficient of saturated components and polar aromatic was higher than that of asphaltenes and aromatic components.

Retrieving Spectra of Pure Components from the DOSY-NMR Experiment via a Comprehensive Approach Involving the 2D Asynchronous Spectrum, 2D Quotient Spectrum, and Genetic Algorithm Refinement.

When diffusion coefficients of different components in a mixture are similar, NMR spectra of pure individual components are difficult to be obtained via a diffusion-ordered spectroscopy (DOSY) experiment. Two-dimensional correlation spectroscopy (2D-COS) is used to analyze the data from the DOSY experiment. Through the properties of the systematic absence of cross-peak (SACP) in the 2D asynchronous spectra, spectra of pure components can be obtained even if their diffusion coefficients are similar. However, fluctuations in peak-position and peak-width are often unavoidable in NMR spectra, which makes SACPs unrecognizable. To address the problem, a 2D quotient spectrum is used to identify the masked SACPs. However, undesirable interference peaks due to the fluctuations in peak-position and peak-width are still present when we extract a spectrum of a component by slicing the 2D asynchronous spectrum across the SACP. A genetic algorithm (GA) is used to select a suitable subset of spectra where the diversities of peak-position and peak-width are significantly reduced. Then, we used the selected spectra to construct a refined 2D asynchronous spectrum so that the spectra of pure components with significant attenuated interference can be obtained. The above approach has been proven to be effective on a model system and a real-world example, demonstrating that 2D-COS possesses a bright perspective in the analysis of the bilinear data from DOSY experiments.

In preprints: morphogens in motion.

In preprints: morphogens in motion.

The Effective Diffusion Coefficient of Hydrogen in Tungsten: Effects of Microstructures From Phase-Field Simulations

In this work, we propose an efficient numerical method to study the effects of microstructures on the effective diffusion coefficient of the diffusion component in materials. We take the diffusion of hydrogen (H) atoms in porous polycrystalline tungsten (W) as an example. The grain structures and irradiated void microstructures are generated by using the phase-field model. The effective diffusion coefficients of H in these microstructures are obtained by solving the steady-state diffusion equation, using a spectral iterative algorithm. We first validate our simulation code for calculating the effective diffusion coefficient by using three simple examples. We then investigate the effects of the grain morphology and porosity on the effective diffusion coefficient of H in W. Regardless of whether the grain boundary is beneficial to the diffusion of H or not, it is found that the effective diffusion coefficient of H along the elongated grain direction in columnar crystals is always greater than that in isometric crystals. The increase of the porosity can significantly decrease the effective diffusion coefficient of H from the simulations of the porous W. A correlation of converting the two-dimensional (2D) effective diffusion coefficient into three-dimensional (3D) in the porous and polycrystalline W is fitted by using our simulation data, respectively. Two fitted correlations can be used to predict the synergistic effect of the porosity and grain boundary on the effective diffusion coefficient of H in W. Consequently, our simulation results provide a good reference for understanding the influence of the complex microstructures on H diffusion, and may help to design W-based materials for the fusion reactor.

INSTABILITY OF MECHANICAL EQUILIBRIUM AND SOME FEATURES OF CONCENTRATION CONVECTION IN ISOTHERMAL TERNARY GAS MIXTURES

Experimental study of the occurrence of convective flows in a three-component gas mixture He + R12 – Ar at various pressures and concentrations of the miscible components has been carried out. It is shown that the intensity of convective flows increases with increasing pressure. It is noted that in the system under consideration, the occurrence of convective flows is possible when the content of Freon-12 in the mixture is more than 0.1 mole fraction. A numerical study of the instability of mechanical equilibrium in the system He + R12 – Ar with significantly different diffusion coefficients of gas mixture components has been carried out by means of the splitting scheme in terms of physical parameters. The presented mathematical model makes it possible to describe the process of formation of a convective structure for various compositions of mixture. The onset of instability is accompanied by the appearance of nonlinear isoconcentration lines. Within the numerical framework, the onset times of various mixing regimes are determined.

Apparent diffusion coefficient and intravoxel incoherent motion-diffusion kurtosis model parameters in invasive breast cancer: Correlation with the histological parameters of whole-slide imaging

ObjectivesTo evaluate the correlation of ADC and IVIM-diffusion kurtosis (DK) model parameters with quantitative histological parameters of whole-slide imaging (WSI). MethodsThis retrospective study (September 2015–July 2016) included 37 consecutive patients (all females; median age: 64 years, range, 41–82 years), each with a single invasive breast ductal carcinoma lesion with a mass appearance on preoperative MRI. DWI with b-values of 0, 50, 100, 300, 550, 850, and 1000 s/mm2 was performed. ADC maps were generated with b-values of 50 and 850 s/mm2. The IVIM-DK model was analysed using the following formula:Sb=S0fe−bD∗+1−fe−bD+1/6kbD2where S is the signal intensity, b is the b-value, f is the perfusion fraction, D* is the pseudo-diffusion coefficient of the vascular component, D is the diffusion coefficient of the non-vascular component, and k is the diffusion kurtosis. Whole tumour segmentation was performed to obtain the mean ADC, f, D*, D, and k. Quantitative histological parameters were obtained using cytokeratin immunostaining and WSI. The correlation of ADC and IVIM-DK model parameters with quantitative histological parameters was examined by Pearson's correlation. ResultsThe ADC was significantly correlated with the area ratio of interstitium (r = 0.53, p = 0.00082) and entropy (r = −0.58, p = 0.00019). k was significantly correlated with the area ratio of cancer cell nuclei (r = 0.53, p = 0.00079). ConclusionsSince the ADC reflected the area ratio of interstitium and entropy, and diffusion kurtosis reflected the area ratio of cancer cell nuclei, these parameters may be effective in distinguishing between benign and malignant breast tumours and in grading breast cancer.