Effect of ring-shaped clusters on magnetic hyperthermia: modelling approach

Experiments demonstrate that magnetic nanoparticles, embedded in a tissue, very often form heterogeneous structures of various shapes and topologies. These structures (clusters) can significantly affect macroscopical properties of the composite system, in part its ability to generate heat under an alternating magnetic field (so-called magnetic hyperthermia). If the energy of magnetic interaction between the particles significantly exceeds the thermal energy of the system, the particles can form the closed ring-shaped clusters. In this work, we propose a relatively simple model of the heat production by the particles united in the ‘ring’ and immobilized in a host medium. Mathematically, this model is based on the phenomenological Debye equation of kinetics of the particles remagnetization. Magnetic interaction between all particles in the cluster is taken into account. Our results show that the appearance of the clusters can significantly decrease the thermal effect. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

Nonlinear dispersive cell model for microdosimetry of nanosecond pulsed electric fields

For applications based on nanosecond pulsed electric fields (nsPEFs), the underlying transmembrane potential (TMP) distribution on the plasma membrane is influenced by electroporation (EP) of the plasma membrane and dielectric dispersion (DP) of all cell compartments which is important for predicting the bioelectric effects. In this study, the temporal and spatial distribution of TMP on the plasma membrane induced by nsPEFs of various pulse durations (3 ns, 5 ns unipolar, 5 ns bipolar, and 10 ns) is investigated with the inclusion of both DP and EP. Based on the double-shelled dielectric spherical cell model, the Debye equation describing DP is transformed into the time-domain form with the introduction of polarization vector, and then we obtain the time course of TMP by solving the combination of Laplace equation and time-domain Debye equation. Next, the asymptotic version of the Smoluchowski equation is included to characterize the EP of plasma membrane in order to observe more profound electroporation effects with larger pore density and electroporated areas in consideration of both DP and EP. Through the simulation, it is clearer to understand the relationship between the applied nsPEFs and the induced bioelectric effects.

Nonlinear Dispersive Cell Model for Microdosimetry of Nanosecond Pulsed Electric Fields

For nanosecond pulsed electric fields (nsPEFs) based application, the underlying transmembrane potential (TMP) distribution of the plasma membrane is influenced by electroporation (EP) of the plasma membrane and dispersion (DP) of all cell compartments and is important for predicting the bioelectric effects. In this study, we analysed temporal and spatial distribution of TMP induced by nsPEFs of various durations (3 ns, 5 ns unipolar, 5 ns bipolar, and 10 ns) with the consideration of both DP and EP. Based on the double-shelled dielectric spherical cell model, we used second-order Debye equation to characterize the dielectric relaxation of plasma membrane and nuclear membrane in the frequency domain and transformed the Debye equation into the time domain with the introduction of polarization vector, then we obtained the time course of TMP by solving the combination of Laplace equation and time-domain Debye equation. Next, we used the asymptotic version of the smoluchowski equation to characterize electroporation of plasma membrane and added it to our model to achieve the temporal and spatial distribution of TMP and pore density. Much faster and more pronounced increased in TMP can be found with the consideration of dielectric relaxation of plasma membrane and nuclear membrane, and much larger electroporated area of at least half of the plasma membrane was obtained with the consideration of both DP and EP. Through the simulation it is clearer to understand the relationship.

Dielectric materials

The macroscopic and microscopic approaches to determining polarization are explained. The types of polarization, frequency response, and anomalous dispersion are discussed. The Debye equation for orientational polarization is derived. The concept of effective field is introduced. The dispersion equations for acoustic waves and for optical phonons are derived. The properties of piezoelectricity, pyroelectricity, and ferroelectricity are discussed. The attenuation of optical fibres, the operation of a photocopier, and the ability of liquid crystals to rotate polarization are also discussed.

Preferred Orientation, PDF and Debye Equation

The effect of preferred orientation is currently neglected in the Debye Equation and PDF calculations. This is to a large extend justified, especially for the PDF, as the scattering by large sample volumes is detected by an area detector. The integration of powder rings reduces the effects of preferred orientation. As more laboratory PDF measurements become available that use linear position sensitive detectors or single counter detectors, preferred orientation needs to be reconsidered. A Rietveld calculation treats preferred orientation by multiplying the Bragg intensity by a factor that depends on the angle between the reciprocal space vector and the preferred orientation axis. The powder intensity I(Q) is thus multiplied by a complex function that depends at each Q on the degree of preferred orientation, the lattice parameters, reflection multiplicity etc. The effect on the PDF is therefore the convolution by the Fourier transform of this complex function. The Debye equation is derived from a spherical average of the scattering intensity of a finite object. Thus completely random orientation of the powder grains is implicitly assumed. Both, the Debye algorithm and the PDF algorithm calculate the powder pattern, respectively the PDF from a histogram of interatomic distances, which correspond to a spherical average of all interatomic distance vectors. This histogram does not allow for a Rietveld preferred orientation correction. The effects of preferred orientation on the PDF will be presented on the basis of simulated diffraction pattern. An algorithm to describe the changes in the PDF and the inverse sine Fourier transform as a convenient tool to calculate the powder diffraction pattern will be introduced. This is a good alternative to the Debye equation and allows to take preferred orientation into account both for the PDF and the calculated powder.

Noninvasive Measurement of Temperature Distribution in a Pipe by Using Electrical Capacitance Tomography

This study has launched a concept to measure real time two-dimensional temperature distribution non-invasively by a combination of electrical capacitance tomography (ECT) technique and Debye equation. The concept has two steps which are the relative permittivity calculation from the measured capacitance among the many electrodes by ECT technique, and the temperature distribution calculation from the relative permittivity distribution by Debye equation. ECT sensor with 8 or 12-electrode is designed to measure and visualize the cross sectional temperature distribution in heating water as a basic experiment and melting polycarbonate pellets as a main experiment. Consequently, it is found that the water capacitance is changed by 1.14×10−6F as every 1.0 degree Celsius water temperature change. Moreover, the images of the temperature distribution from the relative permittivity distribution are reconstructed at every time step during the polycarbonate melting process. The non-invasive temperature values by a combination of ECT technique and Debye equation were compared with the invasive temperature values by the thermocouples. The non-invasive values have a good agreement with the invasive values by approximate 5%.

Domain structure investigation of non-stoichiometric strontium ferrites and cobaltites

Monte Carlo domain structure simulation and Debye equation calculation of XRD patterns were used to confirm the formation of domain structure and investigate its peculiarities. Correspondence of simulated XRD patterns with synchrotron powder diffraction experiments is achieved on the conditions that beside of 90o rotations of brownmillerite-like domains inside perovskite-like matrix each domain contains areas with perpendicularly oriented tetrahedral chains. Influence of such parameters as stoichiometry, average domain size, orthorhombic distortion degree on the XRD patterns is considered.