Showing papers by "Dragan Poljak published in 2022"

Uncertainty quantification and sensitivity analysis of transcranial electric stimulation for 9-subdomain human head model

Abstract: This paper deals with uncertainty quantification of transcranial electric stimulation (TES) of realistic human head model. The head model taken from Visible Human Project consists of 9 subdomains: scalp, skull, CSF, grey matter, white matter, cerebellum, ventricles, jaw and tongue. The deterministic computation of quasi-static induced electric scalar potential features boundary element method (BEM). Conductivities of each subdomain are modelled as uniformly distributed random variables and stochastic analysis features a non-intrusive stochastic collocation method (SCM). The input uncertainties impact only the magnitude of the electric scalar potential and not the position of the potential extrema. Skin and brain conductivities play the most important role, while CSF conductivity has negligible impact on the output potential variance. The significance of the skull conductivity is not high for the chosen input parameter setup. In the previous work authors considered 3-compartment head model which consisted of scalp, skull and brain compartments. The presented model is a step forward in SCM+BEM TES analysis, primarily in terms of model complexity. Comparing the results of the two analyses it can be concluded that the uncertainty in the added tissues’ conductivities do not impact the variation of the output electric potential.

Assessment of Incident Power Density on Spherical Head Model up to 100 GHz

Abstract: This article presents a technique for the accurate assessment of the spatially averaged incident power density (IPD) on a spherical human head model from 3.5 to 100 GHz. The spatially-averaged IPD is defined either by averaging components of the power density vector normal to an evaluation surface, or by averaging its norm. The electromagnetic exposure assessment is provided for a dipole antenna placed at a separation distance of 2–150 mm from the model. We compare the IPD averaged over a proposed spherical surface with differently positioned planar surfaces. Results show that, for appropriate settings of the ex- posure above 6 GHz, the IPD averaged on a spherical surface is up to 12% larger for the normal definition, while marginally lower for the norm definition. In the worst case scenario, the spatially averaged IPD on a spherical surface is up to about 30% larger regardless of the definition. Comparative analysis between the definitions of the IPD averaged on a spherical model demonstrates that the norm definition yields significantly larger values in the reactive near field at characteristic frequencies, whereby this difference is marginal out of the reactive near field.

Review of Least Action Principle in Electromagnetics: Part II: Derivation of Maxwell's Equations

Abstract: The 2nd paper in three-part study deals with a derivation of Maxwell's equations by using Hamilton's principle in electromagnetics and Noether's theorem for fields. Kinematical Maxwell's equations are derived from gauge symmetry, while two dynamical Maxwell's equations are derived by minimizing the functional of electromagnetic energy. The corresponding Lagrangian is given as difference between energy stored in the magnetic and electric field respectively.

Absorbed Power Density in a Multilayer Tissue Model due to Radiation of Dipole Antenna: Part II Results

Abstract: The paper presents results for the induced field and the absorbed power density (Sab) at the surface of the planar multilayer model of the human tissue due to radiation of dipole antenna obtained by means of analytical/numerical approach. The influence of multi-layered domain is taken into account via the Fresnel plane wave reflection/transmission approximation. Numerical procedures pertain to Galerkin-Bubnov Indirect Boundary Element Method (GB-IBEM). Some illustrative examples for various frequencies, dipole lengths and distances of dipole from the interface are given.

Absorbed Power Density in a Multilayer Tissue Model due to Radiation of Dipole Antenna at GHz Frequency Range: Part I Theoretical Background

Abstract: The paper deals with a theoretical background for the assessment of the absorbed power density $(S_{ab})$ in the planar multilayer model of the human tissue due to radiation of dipole antenna based on analytical/numerical approach. The reflecting/transmitting phenomena in multilayer tissue model are taken into account via the corresponding reflection/transmission coefficient stemming from Fresnel plane wave approximation. Radiation of dipole antenna above a multilayer is analysed by solving the Pocklington integro-differential equation and related integral expressions for the radiated electric and magnetic fields. An outline of applied numerical procedure is given, as well.

Transient analysis of multiple straight wires in the presence of a half-space using different time-domain measures

Abstract: The paper deals with a direct time-domain (TD) analysis of multiple wire configurations using various TD measures based on the energy stored in the near field. The currents along the wires are obtained solving the coupled Hallen integral equations. Once the current distribution is determined it is possible to calculate the charge via continuity equation. Knowing the distribution of current and charge along the wires, TD energy measures involving spatial integrals of squared values of transient current and charge, the energy stored in the electric and magnetic fields of wires are evaluated. Then total TD power measure defined as the time derivative of the total energy measure is computed. Finally, according to the definition stemming from the circuit theory the distribution of root-mean-square (RMS) values of transient current is calculated. Some computational examples for transient current, TD energy, and power measures, respectively, and RMS distribution along the wires are presented.

Assessment of Area-Average Absorbed Power Density on Realistic Tissue Models at mmWaves

Abstract: Currently, most state-of-the-art research in computational dosimetry utilizes flat-surface tissue models to simplify the problem geometry and thus mitigate computational complexity. However, depending on the ratio of the penetration depth and the curvature radius, this may lead to a non-correct estimation of the power absorbed by the tissues due to constructive/destructive interference. In this study, we propose an accurate evaluation of the area-average absorbed power density in curved tissue-equivalent models by computing the surface integral of the normal component of the absorbed power density vector field. The numerical analysis is performed for plane wave exposure of an ear model at 60 GHz. We also investigate the effect of the averaging area shape on the absorbed power density by considering 1 cm2 square- and disk-shaped averaging surfaces. Results show a substantial relative difference of 14 % in the area-averaged absorbed power density over a disk-shaped averaging surface between transverse electric and magnetic polarization, with the reference being the value of the area-averaged absorbed power density for a planar homogeneous model and normal incidence. By using the same reference value, negligible differences of 1.81 % and 0.92 % for transverse electric and magnetic polarization, respectively, are present when the averaging area shape changes. According to the studied exposure scenarios, the area-averaged absorbed power density variations as a function of the averaging surface geometry are less significant than those related to the polarization of the incident field.

Modeling the COVID-19 epidemic in Croatia: a comparison of three analytic approaches

Abstract: Aim To facilitate the development of a COVID-19 predictive model in Croatia by analyzing three different methodological approaches. Method We used the historical data to explore the fit of the extended SEIRD compartmental model, the Heidler function, an exponential approximation in analyzing electromagnetic phenomena related to lightning strikes, and the Holt-Winters smoothing (HWS) for short-term epidemic predictions. We also compared various methods for the estimation of R0. Results The R0 estimates for Croatia varied from 2.09 (95% CI 1.77-2.40) obtained by using an empirical post-hoc method to 2.28 (95% CI 2.27-2.28) when we assumed an exponential outbreak at the very beginning of the COVID-19 epidemic in Croatia. Although the SEIRD model provided a good fit for the early epidemic stages, it was outperformed by the Heidler function fit. HWS achieved accurate short-term predictions and depended the least on model entry parameters. Neither model performed well across the entire observed period, which was characterized by multiple wave-form events, influenced by the re-opening for the tourist season during the summer, mandatory masks use in closed spaces, and numerous measures introduced in retail stores and public places. However, an extension of the Heidler function achieved the best overall fit. Conclusions Predicting future epidemic events remains difficult because modeling relies on the accuracy of the information on population structure and micro-environmental exposures, constant changes of the input parameters, varying societal adherence to anti-epidemic measures, and changes in the biological interactions of the virus and hosts.

Stochastic-Deterministic Assessment of Electric Field Radiated by Base Station Antenna above a Two-Layered Ground

Abstract: The paper deals with stochastic-deterministic modelling of radiated electric field by base station antennas (BSAs) operating in GSM frequency range. Within the framework of deterministic analysis, the total electric field above a two-layered lossy ground is obtained by considering the incident and reflected ray in the far field zone. The influence of nonhomogeneous lower medium is taken into account via two approaches: Fresnel plane wave reflection coefficient (FRM) and simplified reflection coefficient stemming from Modified Image Theory (MIT). Antenna height, relative conductivity, and permittivity of each ground layer, as well as the thickness of the upper ground layer, are considered as input parameters with inherent uncertainty. To quantify the uncertainty of output electric field, deterministic models are treated as black boxes by two stochastic methods, Monte Carlo (MC) and Stochastic Collocation (SC), respectively. Stochastic mean and standard deviation of the output are computed, and sensitivity analysis is carried out in order to analyze the impact of input parameters’ variations on the resulting electric field variance. The presented results expose weakness and strength of the two stochastic methods, particularly identifying the cases when the preferred SC method fails to converge. Furthermore, sensitivity analysis reveals that despite the smallest variation around its respective average value, the antenna height has the highest impact on the output variance at observation points in the vicinity of the antenna. However, as the distance from the antenna increases, the 1st layer depth and its relative electric permittivity become the most significant parameters.

Electric Field Radiated By a Vertical Dipole Antenna Above a Lossy Half Space by using Calculated and Assumed Current Distribution

Abstract: This paper compares a numerical model of a vertical dipole placed in the air, along the z-axis, above a lossy half space with a model with assumed current distribution (triangular and sinusoidal). The electric field is computed for various heights above ground and various ratios of the physical length and wavelength of the antenna. The obtained results show that both approaches give similar results under certain conditions.

On 5G Radiated Field Measurement/Calculation Procedures and Exposure Compliance Limits

Abstract: The paper deals with several measurement and calculation procedures applicable in 5G New Radio technology. It brings the comparison of measured and calculated electric field levels for the purpose of simplification of industry field work. The structure of 5G New Radio signal is shortly explained, as well as all applied measurement procedures: Code-Selective Procedure, Frequency-Selective Procedure and Channel Power. The results are presented in 95% confidence interval and compared to the valid limit values. For the purpose of electric field calculation, several approximations procedures are used: Free Space, Perfect Ground Reflection and lossy ground reflection based on reflection coefficients arising from Fresnel and Modified Image Theory approach, respectively. Some illustrative results are given in the paper.

A Simplified Analytical Model for Human Exposure to Electromagnetic Radiation of HF Wireless Power Transmitter

Abstract: In this paper, human body exposure to high frequency (HF) electromagnetic field is analysed. Small loop antenna as a transmitter and human body at defined distance are analytically and numerically modelled. The analysis is carried out for simplified cylinder and realistic human body model settled in free space and exposed to HF radiation in terms of induced current density and induced electric field inside the body at frequency of 6.78 MHz. Analytical approach involves the use of the approximate sinusoidal current distribution and analytical evaluation of field integrals. The results obtained analytically are validated by numerical simulations in commercial software FEKO, based on Method of Moments (MoM). It is shown that there is no significant difference in results while using different approaches (analytical and numerical) which is excellent for theoretical calculations limited on simplified models so both approaches can be used for human body exposure estimation in defined scenarios.

Analysis of SAR in a Simplified Body Model due to a Short Dipole Antenna Radiation

Abstract: The paper deals with an analytical assessment of a whole-body averaged specific absorption rate ($SAR_{WB}$) when human body is illuminated by a short dipole antenna. The body is represented by a simple parallelepiped whose electric properties correspond to relative electric permittivity and electric conductivity of muscle tissue. The antenna-body distance and frequency are changed while the antenna parameters and body geometry are constant. In the computation of transmitted field into the body used for $SAR_{WB}$ calculation, the air-body interface is taken into account by means of transmission coefficient stemming from Modified Image Theory (MIT). First, the theoretical background is outlined and then the results depicting the behaviour of $SAR_{WB}$ with respect to antenna-body distance and frequency are presented. The resulting $SAR_{WB}$ values do not exceed the basic restriction nor for occupational nor for general population.

Does COVID-19 Behave as Lightning Strike?

Abstract: Early stages of an epidemic are characterized by exponential growth in the number of infected cases, corresponding to the effective reproduction number greater than 1. After deliberate interventions in the disease transmission are introduced, the effective reproduction number should drop below 1. The number of active infections should follow the downward trend conditioned by the stringency of the measures and drop exponentially. The growth phase is in general of shorter duration than the decay phase. This asymmetry imposes itself as an aggravating factor onto common mathematical models used to capture the epidemic dynamics. To overcome aforementioned issue, in this paper, we compare the functional form of the epidemic dynamics with the analytical expression often found in the lightning research and standardization. Computational examples are given for different countries that kept track of the number of daily positive cases, recovered cases and deaths during the period of the first outbreak of Coronavirus disease 2019 (COVID-19).

Stochastic-Deterministic Electromagnetic Modeling of Human Head Exposure to Microsoft HoloLens

Abstract: In this paper, the electromagnetic (EM) simulation of the exposure of a spherical model of the human head to the HoloLens, a mixed reality device developed and manufactured by Microsoft, is performed at 10 GHz in addition to IEEE 802.11ac Wi-Fi frequencies of 2.4 and 5 GHz. The compliance assessment with current guidelines and standards for limiting human exposure to EM fields up to 300 GHz by means of incident power density (IPD) is provided at separation distances between the model and antenna ranging from 2.5 to 150 mm. The effect of the curvature of the average adult and child head on the IPD is investigated on a control surface of 4 cm2. Results stemming from stochastic analysis indicate marginal difference between the spatially averaged IPD on the two distinct head models. On the other hand, comparative analysis of the spatially averaged IPD on the least and most curved body parts points to relative differences of up to 20% in certain exposure scenarios. Overall, spherical head models yield significantly higher values of the spatially averaged IPD (up to 25%) compared to standard planar models. It is therefore important to consider the inherent curvature of the nonplanar exposed body parts (e.g., head) to accurately assess targeted exposure quantities.

Transient thermal analysis of human exposure to electromagnetic fields

Abstract: |The study of the thermal effect caused by exposure to electromagnetic (cid:12)elds is a focus of this research. To quantify the induced current and temperature distribution in the human body an assessment tool for the frequency range of 50 Hz to 110 MHz has been developed. The major contribution consists of providing a quantitatively accurate and relatively simple model. The formulation of the problem is based on a simpli(cid:12)ed cylindrical representation de(cid:12)ned by the anatomical parameters of the human body. The bio-thermal modeling is carried out in two stages. Firstly, the electromagnetic analysis is based on the transmission lines (TL) theory. Secondly, a thermal modeling based on the thermal networks model (nodal method) is approached. This allows us to quantify the corresponding thermal gradients in the human body.

Septum Feed Design for Right and Left Circular Polarisation

Abstract: The benefits of circular polarization range from the reduction of the Faraday rotation effect in satellite systems, to the multipath rejection and independence of antenna orientation in the growing applications of unmanned aerial vehicles. Here, the focus is on the septum feed design which can be implemented in the ground dish or horn antennas, or used standalone as an antenna. It provides left and right hand circular polarization and better circular polarization characteristics within the wide frequency band, in relation to the given literature. The analysis and optimisation of the septum feed is done using the analytical approach, numerical simulations and measurements, and the results show that satisfying impedance and radiation parameters are achieved in the wide frequency band from 5.1 – 6.0 GHz.

Calculation of Complex Power Generated by a Transmitting Thin Wire Antenna Radiating above a Lossy Half-space

Abstract: — The paper deals with an efficient approach to determine complex power generated by a thin wire antenna above a lossy ground. Once the current distribution along a thin wire is obtained by numerically solving the Pocklington integro-differential equation the complex power of the antenna can be obtained by solving the integral over the inner product of tangential component of the electric field and current distribution along the wire stemming from Poynting theorem. Numerical calculation procedure uses the vectors and matrices already constructed within the calculation procedure for the current distribution. Some illustrative numerical results for the active power, reactive power and apparent power of the dipole antenna radiating over a lossy half-space are presented in the paper for different values of input parameters.

Review of Least Action Principle in Electromagnetics: Part III: Applications

Abstract: This paper, being 3rd part of the study, deals with an application of variational principle to the solution of problems in electro magnetics. Some applications to canonical problems are given and some general aspects of numerical modeling stemming from variational approach are addressed. Finally, Ritz method of solution is presented with related simple example.

On the Applicability of Numerical Quadrature for Double Surface Integrals at 5G Frequencies

Abstract: —The human exposure assessment to wireless com- munications systems including the fifth generation (5G) mobile systems is related to determining the specific absorption rate (SAR) or the absorbed power density (APD). The assessment of both quantities requires the use of various numerical techniques, including moments method (MoM). As the use of MoM results in a fully populated system matrix, a tremendous computational cost is incurred, both in terms of matrix fill time and memory allocation, as the matrix size is directly related to frequency of the problem. This paper investigates the applicability of numerical integration at frequencies related to 5G. The novelty of this work is related to the comprehensive set of tests of various combination of source and observation triangles using the developed unit cube test. A number of convergence tests were performed to investigate the effects of the increasing frequency and the discretization scheme on the numerical solution, as well as to determine how to curb the computational requirements by the proficient use of numerical integration. The results show that in the lower GHz range, lower integration orders could be used, resulting in the decrease of matrix fill time without loss of solution accuracy.