Limitations of the permeability-limited compartment model in estimating vascular permeability and interstitial volume fraction in DCE-MRI

Dynamic contrast-enhanced magnetic resonance imaging commonly uses compartment models to estimate tissue parameters in general and perfusion parameters in particular. Compartment models assume a homogeneous distribution of the injected tracer throughout the compartment volume. Since tracer distribution within a compartment cannot be assessed, the parameters obtained by means of a compartment model might differ from the actual physical values.This work systematically examines the widely used permeability-surface-limited one-compartment model to determine the reliability of the parameters obtained by comparing them with their actual values. A computer simulation was used to model spatial tracer distribution within the interstitial volume using diffusion of contrast agent in tissue. Vascular parameters were varied as well as tissue parameters. The vascular parameters used were capillary radius (4 and 12 μm), capillary permeability (from 0.03 to 3.3 μm/s) and intercapillary distances from 30 to 300 μm. The tissue parameters used were tortuosity (λ), porosity (α) and interstitial volume fraction (v_e).Our results suggest that the permeability-surface-limited compartment model generally underestimates capillary permeability for capillaries with a radius of 4 μm by factors from ≈0.03 for α=0.04, to ≈ 0.1 for α=0.2, to ≈ 0.5 for α=1.0. An overestimation of actual capillary permeability for capillaries with a radius of 12 μm by a factor of ≥1.3 was found for α=1.0, while α=0.2 yielded an underestimation by a factor of ≈0.3 and α=0.04 by a factor of ≈ 0.03. The interstitial volume fraction, v_e, obtained by the compartment model differed with increasing intercapillary distances and for low vessel permeability, whereas v_e was found to be estimated approximately accurately for P=0.3 μm/s and P=3.3 μm/s for vessel distances <100 μm.     

An interpretation of structural sorting diagrams for AB type compounds using molecular orbital ideas

The factors governing the structure adopted by a particular AB compound are investigated by deriving two parameters reflecting aspects of the interaction between A and B, using simple molecular orbital ideas, which can be quantified by use of atomic parameters derived from pseudopotential theory. A plot of the values of these two parameters, for a large database of compounds, produces a remarkable topological clustering of AB compounds with the same structure. This structural sorting can also be effected for nonoctet AB compounds if the number of electrons is taken into account. These parameters are related to other indices, R_σ, R_π, previously used by Bloch, Zunger, Phillips et al. to construct structural sorting diagrams. Hence we find a justification for the success of such displays, and shed light on the reasons underpinning structural preference, in terms of the number of valence electrons, and the relative positions of the energy levels of the constituent atoms. There appear to be strong similarities between the electronic reasons behind atomic site preferences in molecules and this site preference or coordination number problem in solids.     

Non-linear time domain model of electropermeabilization: Response of a single cell to an arbitrary applied electric field

Background: Electroporation is now a common tool in biotechnology and is used in a number of medical treatments. Until recently, the development of theoretical models of electroporation has lagged behind the experimental research. In order to optimize the efficiency of electroporation, it is important to consider as many biological and physical aspects as possible and it is a necessity that a variety of electric pulse parameters be tried. Thus a comprehensive model which can predict electropermeabilization as a result of any form of applied electric field and other important electroporation parameters is necessary.Results: A numerical model for a single cell electroporated by application of arbitrary external electric field pulses has been developed. The model is used to compare the transmembrane potential Vm, and pore density N, developed in response to the pulses. Vm and N are calculated via a piece-wise step response method that enables solutions to be obtained for any practical applied electric field waveform. Pore density is shown to increase so long as a threshold Vm is maintained by the electric field, and effectively clamps Vm to just over 1 V while N is increasing. Short unipolar pulses are also shown to create asymmetrical N between the two cell polar regions, whereas bipolar pulses result in a symmetrical N.Conclusions: The model presented here helps predict dynamic non-linear results of electropermeabilization, given any form of applied electric field and other important electroporation system parameters. This model can be used as a tool for the determination of starting parameters in biological applications.     

Langevin fission dynamics of hot rotating nuclei: Systematic application to Z 2/A=34–42 heavy nuclei

A stochastic approach that treats fission dynamics on the basis of three-dimensional Langevin equations is used to calculate the mass-energy distributions of fragments originating from the fission of compound nuclei whose fissility parameter lies in the range Z ²/A=34–42. In these calculations, use was made of the liquid-drop model allowing for finite-range nuclear forces and the diffuseness of the nuclear surface in calculating the potential energy and a modified one-body mechanism of viscosity in describing dissipation. The emission of light prescission particles is taken into account on the basis of the statistical model. The calculations performed within three-dimensional Langevin dynamics reproduce well all parameters of the experimental mass-energy distributions of fission fragments and all parameters of the prefission-neutron multiplicity for various parameters of the compound nucleus. The inclusion of the third collective coordinate in the Langevin equations leads to a considerable increase (by up to 40–50%) in the variances of mass-energy distributions in relation to what was previously obtained from two-dimensional Langevin calculations. For the parameters of the mass-energy distributions of fission fragments and the parameters of the prefission-neutron multiplicity to be reproduced simultaneously, the reduction coefficient K _s must be diminished at least by a factor of 2(0.2≤K _s ≤0.5) in relation to that in the case of total one-body viscosity (K _s =1).     

Bayesian methods for parameter estimation in effective field theories

We demonstrate and explicate Bayesian methods for fitting the parameters that encode the impact of short-distance physics on observables in effective field theories (EFTs). We use Bayes’ theorem together with the principle of maximum entropy to account for the prior information that these parameters should be natural, i.e., O(1) in appropriate units. Marginalization can then be employed to integrate the resulting probability density function (pdf) over the EFT parameters that are not of specific interest in the fit. We also explore marginalization over the order of the EFT calculation, M, and over the variable, R, that encodes the inherent ambiguity in the notion that these parameters are O(1). This results in a very general formula for the pdf of the EFT parameters of interest given a data set, D. We use this formula and the simpler “augmented χ²” in a toy problem for which we generate pseudo-data. These Bayesian methods, when used in combination with the “naturalness prior”, facilitate reliable extractions of EFT parameters in cases where χ² methods are ambiguous at best. We also examine the problem of extracting the nucleon mass in the chiral limit, M₀, and the nucleon sigma term, from pseudo-data on the nucleon mass as a function of the pion mass. We find that Bayesian techniques can provide reliable information on M₀, even if some of the data points used for the extraction lie outside the region of applicability of the EFT.     

Effects of Dzyaloshinskii-Moriya interaction on thermal entanglement and teleportation via a two-qubit Heisenberg XXZ spin chain under external magnetic field

This paper mainly investigates the effects of different Dzyaloshinskii-Moriya (DM) anisotropic antisymmetric interactions on thermal entanglement and teleportation of one-qubit state in both the standard and non-standard protocols as well as the partial teleportation of an entangled state via a two-qubit Heisenberg XXZ spin chain in the presence of external magnetic fields. The dependency of the thermal entanglement and average fidelity on various system parameters is analyzed. The interplay of the different parameters on the teleportation is discussed. The DM interaction is found to be effective for the thermal entanglement in the spin chain both with and without external magnetic fields. However, it turned out to be destructive for the teleportation in the standard protocol, whereas is found constructive for single qubit teleportation when the spin chain with the z-direction parameters is used as the channel in the non-standard protocol. Moreover, the results show that, for teleporting one-qubit state, the antiferromagnetic (AFM) chain is the only qualified candidate in the standard protocol, while both the AFM and ferromagnetic (FM) chains with the parameters along the z-axis are all suitable in the non-standard protocol when the parameters are chosen appropriately. For the partial teleportation of entanglement, both the AFM and FM chains are eligible as long as the appropriate combinations of parameters are chosen. In addition, the comparison of the effects of the same, fixed x- and z-component parameters of the DM interaction (D_x and D_z) on teleportation is presented.     

Behaviour of single-particle states and their eigenvalues near zero energy

For a state in a single-particle potential we derive simple expressions that the eigenvalue behavior and normalization integral properties near threshold. For the square-well, the various parameters in these expressions can be derived analytically. For the more realistic Saxon-Woods well-shape, we have made numerical calculations for s- and p-states and obtained values of these parameters and give rules for their evaluation. We show that those parameters determining the negative energy eigenvalues are also involved in determining the positive energy behavior, and the normalization properties. These studies have direct relevance to recent theories of some types of (d, p) and (n, γ) reactions which critically involve threshold behavior.     

Decoupling of heavy quarks in quantum chromodynamics

Decoupling of heavy quarks in quantum chromodynamics (QCD) defined by mass-independent renormalization is investigated. The structure of the relations between the parameters of f flavour QCD and the parameters of the effective f ? 1 flavour QCD below a heavy-quark threshold is discussed to all orders in the loop expansion, and the relations are computed to two-loop approximation for the minimal subtraction schemes (MS) and to one-loop approximation for some Weinberg schemes. These matching relations can be used to systematically determine the renormalization group (RG)-invariant parameters of the effective theory in terms of the RG-invariant parameters of the theory which includes the heavy quark, or vice versa. For the $\text{MS}$ scheme the connection between Λ_{f ? 1} nad Λ_f to two and three loops is given as well as the two-loop connection between the RG-invariant mass parameters of the f ? 1 and f flavour theory. The effect of heavy quarks on the evolution of the QCD coupling is of significance for present QCD phenomenology based on next-to-leading-order perturbation theory. This is illustrated with a few examples within the $\text{MS}$ scheme.     

Equation of state of a real gas

It is shown using 28 gases as an example that the Van der Waals equation in the form $$\left[ {P + \frac{a}{{(V + c)^k T^m }}} \right](V - b) = RT$$ correctly expresses quantitative relations between parameters P, V, and T for real gases. Here, a, b, and c are constants; k is a number close to 2; and m varies in the range 0.2–2.17 for different gases. The critical parameters of most gases calculated by this formula are found to be close in value to the experimental parameters.     

N-point functions and low-energy scattering by N centres

The scattering of a low-energy particle by a potential of a small range is known to be described satisfactorily by the s-wave alone. In the present paper we give a method of describing low-energy scattering by N potentials with the aid of N waves. For this purpose, a special system of Laplacian eigenfunctions is suggested. The scattering amplitude depends on only N parameters, irrespective of overlapping of potentials. The physical significance of these parameters δ_λ, λ=1,2,…N, is shown by exp (2iδ_λ)=S_λ where S_λ is the eigenvalue of the S matrix. The parameters δ_λ may be obtained by direct methods and perturbation theory.The low-energy scattering by an arbitrary configuration of N centres is discussed. The differential cross-section is averaged over all orientations of the configuration and radially about the direct beam, giving it as a function of the scattering angle. This formula may be used for the phase shift analysis.     

Dispersion parameters and nonlinear optical properties of silicon nitride rib waveguides

Silicon nitride rib waveguides are numerically studied by use of a full-vectorial mode solver program based on finite difference method. Dispersion parameters, up to the third-order, are computed for waveguides of heights 0.8 μm, 0.9 μm, and 1 μm. Like silicon-on-insulator waveguides, silicon nitride rib waveguides allow us to tailor dispersion parameters at telecom wavelengths. Deeply-etched silicon nitride rib waveguides of height up to 1.5 μm are investigated for correct geometries to achieve polarization independence. The computations lead to a minimum etch depth which can be written as linear function of the waveguide height. Etch-depth and waveguide height dependencies of the nonlinear refractive index coefficient of the silicon nitride are studied. It is shown that third-order optical nonlinearities in silicon nitride rib waveguides can be enhanced by suitable choices of waveguide parameters.     

Influence of parallel nozzle electroencapsulation parameters on microcapsule properties – A case study using the Taguchi robust design method

The production of microcapsules by electrospraying two immiscible liquids from oppositely charged parallel nozzles and the subsequent microcapsule collection constitute an electroencapsulation process influenced by numerous parameters. The electroencapsulation parameters include the liquid properties, e.g. bulk liquid conductivity K, viscosity η, density ρ, and surface tension γ; the electric field, gravity field, and the electrospraying and collection geometries; and the atmospheric properties. In the present work, NaI-doped glycerol was used as core liquid, with an optional payload of dispersed thermally carbonized porous silicon nanoparticles (PSi). Chloroform with dissolved Eudragit E 100 cationic copolymer and dispersed talc particles as an anti-tacking agent was used as shell liquid. The influence of varying ten electrospraying parameters (liquid flow rates Q_i, electrospraying voltages |U_i| and polarity, solid concentrations, and temperature T) within the cone-jet mode regime on the structure and yield of microcapsules produced by parallel nozzle electroencapsulation was investigated simultaneously using the Taguchi robust design method. Of the investigated parameters, the most important were found to be NaI concentration and T, both influencing the core liquid conductivity; and the liquid flow rates. The Taguchi experiment and additional results suggest that optimally, the parameters affecting liquid conductivities should be set for a coarse atomization current balance when using a maximal shell liquid flow rate. Then, the core liquid flow rate can be adjusted for best process efficiency.     

Sensitivity analysis in lightning protection risk management

The total risk R can be expressed by the following equation: R = NPL, where N is the number of dangerous events, P is the probability of damage and L measures the amount of loss. These parameters can be regarded as macroparameters in the sense that they can be given as a function of additional parameters (microparameters).Methods of calculation, check and refinement of parameter values have always been general themes of the standardization. The comparison of standards IEC 62305-2:2006 Ed. 1 and IEC 62305-2:2010 Ed. 2 is a good example of these efforts, as changes underwent in the determination of the collection area of service and the value of some parameters, moreover new parameters were introduced in order to break existent parameters into more components.Though the international standard contains the value of parameters, it does not give any information about the procedure how these values were determined, nor about the theoretical considerations behind. Therefore it is proper to ask whether the changes of a given parameter value or introduction of a new parameter make radical changes in resulting risk value or not.In this study sensitivity analysis was used to investigate how the individual macro- and micro parameters influence the risk. Moreover it was determined whether or not new parameters and calculations have an effect on the importance of the respective components of the resulting risk.The sensitivity analysis was done for two case studies in the standard, a country house and an office building respectively, with both editions of the standard.     

Influence of microscopic parameters of chiral molecules on the first-order hyperpolarizability

One-electron model is chosen to analyze the second harmonic response of an organic inclusion complex - urea l-malic acid (ULMA). ULMA has broad transparent region and large nonlinear optical coefficient and damage threshold. Based on the ULMA crystal structure, the model parameters are determined using the unit cell parameters. Numerical results show that the contribution of electric-field to the first-order hyperpolarizability β is larger than that of magnetic-field but the contribution of magnetic-field is important and cannot be neglected. Modeling parameters pitch ξ and radius ρ are found to be involved in the position of peak of β. The peak position of β undergoes red-shift with increasing of ρ and blue-shift with the increasing of ξ. It suggests that the expected nonlinear optical response of a chiral molecule can be obtained through molecular modification to adjust ξ and ρ. Therefore, a chiral molecule may be a favorable host to afford organic inclusion complex with superb nonlinear optical properties.     

Determination of Parameters for an Entropy-Based Atrial Fibrillation Detector

Entropy algorithm is an important nonlinear method for cardiovascular disease detection due to its power in analyzing short-term time series. In previous a study, we proposed a new entropy-based atrial fibrillation (AF) detector, i.e., Entropy_AF, which showed a high classification accuracy in identifying AF and non-AF rhythms. As a variation of entropy measures, Entropy_AF has two parameters that need to be initialized before the calculation: (1) tolerance threshold r and (2) similarity weight n. In this study, a comprehensive analysis for the two parameters determination was presented, aiming to achieve a high detection accuracy for AF events. Data were from the MIT-BIH AF database. RR interval recordings were segmented using a 30-beat time window. The parameters r and n were initialized from a relatively small value, then gradually increased, and finally the best parameter combination was determined using grid searching. AUC (area under curve) values from the receiver operator characteristic curve (ROC) were compared under different parameter combinations of parameters r and n, and the results demonstrated that the selection of these two parameters plays an important role in AF/non-AF classification. Small values of parameters r and n can lead to a better detection accuracy than other selections. The best AUC value for AF detection was 98.15%, and the corresponding parameter combinations for Entropy_AF were as follows: r = 0.01, n = 0.0625, 0.125, 0.25, or 0.5; r = 0.05 and n = 0.0625, 0.125, or 0.25; and r = 0.10 and n = 0.0625 or 0.125.     

A scaling limit with many noncommutativity parameters

We derive the worldsheet propagator for an open string with different magnetic fields at the two ends, and use it to compute two distinct noncommutativity parameters, one at each end of the string. The usual scaling limit that leads to noncommutative Yang–Mills can be generalized to a scaling limit in which both noncommutativity parameters enter. This corresponds to expanding a theory with U(N) Chan–Paton factors around a background U(1)^N gauge field with different magnetic fields in each U(1).