Analytic SAR computation in a multilayer elliptic cylinder for bioelectromagnetic applications.

The specific absorption rate (SAR) is usually considered as the basic quantity to derive the reference levels for the exposure of workers and general population. In this paper, we propose an analytical procedure for the SAR computation inside a biological elliptic cylinder model made up of layers of different biological tissues. The procedure makes it possible to obtain accurate SAR values in simplified models of biological subsystems, and it is also helpful to test numerical techniques to be used for more realistic models and to generate synthetic input data for diagnostic methodologies. For the assumed model, the calculation of the analytical solution has been obtained by generalizing a known procedure that deals only with lossless materials, and the model makes possible the calculation of the SAR for realistic human tissues. Various calculations prove the reliability of the technique.     

Numerical modeling and dosimetry of the 35 mm Petri dish under 46 GHz millimeter wave exposure

Experimental studies on effects of millimeter wave (MMW) exposure on cells cultured in Petri dishes have attracted interest in recent decades. To improve the quantification of the biological responses toward the MMW energy, an accurate and precise MMW dosimetry is to be provided. By using the finite difference time domain (FDTD) method, the numerical dosimetry is performed for a typical 35 mm Petri dish under 46 GHz continuous MMW exposure from an irradiator of a specified power pattern. With the aim of building a precise model, the meniscus at the interface between the culture solution and the Petri dish sidewall is taken into account, followed by the modeling of smooth edges of the Petri dish. The trilinear interpolation is introduced to assist the FDTD method to obtain a more precise dosimetric assessment. The specific absorption rate (SAR) distributions in the cornea cells covered by culture solution in the Petri dish are calculated and compared to display the effects of using Petri dish models of various precision and the trilinear interpolation on dosimetry results. In addition, the SAR distribution in the cells is analyzed to study its homogeneity. The results indicate that the precise Petri dish model and the application of the trilinear interpolation are helpful in improving the precision of numerical dosimetry. It is also revealed that the inhomogeneity of the SAR distribution is well beyond neglect, which deserves cautious consideration in experiments investigating MMW effects on cells in vitro.     

Development of a rat head exposure system for simulating human exposure to RF fields from handheld wireless telephones

The aim of this project was to develop an animal exposure system for the biological effect studies of radio frequency fields from handheld wireless telephones, with energy deposition in animal brains comparable to those in humans. The finite‐difference time‐domain (FDTD) method was initially used to compute specific absorption rate (SAR) in an ellipsoidal rat model exposed with various size loop antennas at different distances from the model. A 3 × 1 cm rectangular loop produced acceptable SAR patterns. A numerical rat model based on CT images was developed by curve‐fitting Hounsfield Units of CT image pixels to tissue dielectric properties and densities. To design a loop for operating at high power levels, energy coupling and impedance matching were optimized using capacitively coupled feed lines embedded in a Teflon rod. Sprague Dawley rats were exposed with the 3 × 1 cm loop antennas, tuned to 837 or 1957 MHz for thermographically determined SAR distributions. Point SARs in brains of restrained rats were also determined thermometrically using fiberoptic probes. Calculated and measured SAR patterns and results from the various exposure configurations are in general agreement. The FDTD computed average brain SAR and ratio of head to whole body absorption were 23.8 W/kg/W and 62% at 837 MHz, and 22.6 W/kg/W and 89% at 1957 MHz. The average brain to whole body SAR ratio was 20 to 1 for both frequencies. At 837 MHz, the maximum measured SAR in the restrained rat brains was 51 W/kg/W in the cerebellum and 40 W/kg/W at the top of the cerebrum. An exposure system operating at 837 MHz is ready for in vivo biological effect studies of radio frequency fields from portable cellular telephones. Two‐tenths of a watt input power to the loop antenna will produce 10 W/kg maximum SAR, and an estimated 4.8 W/kg average brain SAR in a 300 g medium size rat. Bioelectromagnetics 20:75–92, 1999. © 1999 Wiley‐Liss, Inc.     

A study of absorption of energy of the extremely high frequency electromagnetic radiation in the rat skin by various dosimetric methods and approaches

Using experimental and theoretical methods of dosimetry, the energy absorption of extremely high-frequency electromagnetic radiation (EHF EMR) in the skin of laboratory rats was analyzed. Specific absorption rate (SAR) in the skin was determined on the basis of both microthermometric measurements of initial rates of temperature rise in rat skin induced by the exposure and microcalorimetric measurements of specific heat of the skin. Theoretical calculations of SAR in the skin were performed with consideration for dielectric parameters of rat skin obtained from the measurements of the standing wave ratio upon reflection of electromagnetic waves from the skin surface and for the effective area of stationary overheating measured by infrared thermography. A numerical method was developed to determine electromagnetic wave energy reflected, absorbed, and transmitted in the model of flat layers. The algorithm of the method was realized in a computer program and used to calculate SAR in the skin on the basis of the complex dielectric constant of rat skin. The SAR values obtained from experimental measurements, theoretical calculations and numerical analysis are in good mutual correspondence and make about 220-280 W/kg at a frequency of 42.25 GHz and a power of 20 mW at the radiator output. The results obtained can be used for dosimetric supply of biomedical experiments on studying the physicochemical mechanisms of the biological effects of EHF EMR.     

An optimal stopping approach for onset of fish migration

Comprehending life history of migratory fish, onset of migration in particular, is a key biological and ecological research topic that still has not been clarified. In this paper, we propose a simple mathematical model for the onset of fish migration in the context of a stochastic optimal stopping theory, which is a new attempt to our knowledge. Finding the criteria of the onset of migration reduces to solving a variational inequality of a degenerate elliptic type. As a first step of the new mathematical modeling, mathematical and numerical analyses with particular emphasis on whether the model is consistent with the past observation results of fish migration are examined, demonstrating reasonable agreement between the theory and observation results. The present mathematical model thus potentially serves as a simple basis for analyzing onset of fish migration.     

Chemotography for multi-target SAR analysis in the context of biological pathways

The increasing amount of chemogenomics data, that is, activity measurements of many compounds across a variety of biological targets, allows for better understanding of pharmacology in a broad biological context. Rather than assessing activity at individual biological targets, today understanding of compound interaction with complex biological systems and molecular pathways is often sought in phenotypic screens. This perspective poses novel challenges to structure-activity relationship (SAR) assessment. Today, the bottleneck of drug discovery lies in the understanding of SAR of rich datasets that go beyond single targets in the context of biological pathways, potential off-targets, and complex selectivity profiles. To aid in the understanding and interpretation of such complex SAR, we introduce Chemotography (chemotype chromatography), which encodes chemical space using a color spectrum by combining clustering and multidimensional scaling. Rich biological data in our approach were visualized using spatial dimensions traditionally reserved for chemical space. This allowed us to analyze SAR in the context of target hierarchies and phylogenetic trees, two-target activity scatter plots, and biological pathways. Chemotography, in combination with the Kyoto Encyclopedia of Genes and Genomes (KEGG), also allowed us to extract pathway-relevant SAR from the ChEMBL database. We identified chemotypes showing polypharmacology and selectivity-conferring scaffolds, even in cases where individual compounds have not been tested against all relevant targets. In addition, we analyzed SAR in ChEMBL across the entire Kinome, going beyond individual compounds. Our method combines the strengths of chemical space visualization for SAR analysis and graphical representation of complex biological data. Chemotography is a new paradigm for chemogenomic data visualization and its versatile applications presented here may allow for improved assessment of SAR in biological context, such as phenotypic assay hit lists.     

Prediction of electromagnetic field distributions inside biological bodies by using an inverse scattering procedure based on a statistical cooling algorithm

This paper presents an inverse scattering procedure based on a statistical cooling algorithm to predict the electromagnetic field inside a biological body. By knowing only the scattered electric field distribution in a set of observation points external to the biological model, this method seems to be able to predict the electromagnetic field distributions in the investigation domain, minimizing a suitable cost function. To this end, a numerical statistical procedure is used, which allows to treat functions with a large number of unknowns in an efficient manner and to exploit the so called a priori knowledge in the reconstruction process. Some preliminary results are reported, concerning simplified biological geometries, which clearly show the capabilities and effectiveness, and also the current limitations of the proposed approach. Finally, further advances for the proposed imaging technique are indicated and discussed.     

A Resonant System for In Vitro Studies Emulating Wireless Power Transfer Exposure at 13.56 MHz

This paper presents the design of a resonant system for in vitro studies to emulate the exposure of a monolayer of cells to a wireless power transfer system operating at 13.56 MHz. The design procedure targets a system, which maximizes the specific absorption rate (SAR) uniformity on the plane where the layer is cultured, as well as SAR efficiency (defined as SAR over the input power), within the size constraints of a standard incubator. Three resonant wireless power transfer systems with different commonly used loop/coil geometries (cylindrical with circular and square cross-sections and annular) were compared with assess the configuration maximizing the considered design criteria. The system performance in terms of reflection and transmission coefficients, as well as generated E- and H-fields, was characterized numerically and experimentally inside the incubator. Moreover, SAR was computed at the monolayer level. The system equipped with cylindrical coils with square cross-sections led to a high electromagnetic field uniformity in in vitro biological samples. In particular, the uniformities in E and SAR at the layer level were within 7.9% and 5.5%, respectively. This was achieved with the variation in H below the usually considered ±5% limit. © 2020 Bioelectromagnetics Society     

A new in vitro exposure device for the mobile frequency of 900 MHz

A wire patch cell has been designed for exposing cell cultures during in vitro experiments studying possible effects of mobile radio telephone. It is based on the wire patch antenna which works at 900 MHz with a highly homogeneous field inside the antenna cavity. The designed cell structure is symmetric and provides a rather homogeneous field distribution in a large area around its centre. Moreover, the exposure cell can irradiate equally up to eight 35 mm Petri dishes at the same time, which enhances the statistical biological studies. To improve the specific absorption rate (SAR) homogeneity inside each sample, each dish is placed into another 50 mm dish. This way, SAR inhomogeneity is always proper for biological studies (below 30%). The main advantage of this new device is that it can provide SAR levels 20 times higher than those induced by classical Crawford transverse electromagnetic (TEM) cell. Moreover, this small open device is easy to construct and fits into an incubator. However, to be used for in vitro, the wire patch cell is a radiating element with the same radiating pattern as a dipole, and thus some absorbing materials are necessary around the system when used for in vitro experiments. Secondly, because of its narrow bandwidth, it is difficult to maintain its working frequency. To overcome this problem, a matching device is integrated into the test cell. In this paper, we present a detailed explanation of the cell behavior and dosimetric assessments for eight 35 mm Petri dishes exposed. Simulations using the Finite Difference Time Domain technique and experimental investigations have been carried out to design the cell at 900 MHz. The numerical dosimetry was validated by dosimetric measurements. These investigations estimated the dosimetric precision at 11%.     

Multi-stage sampling for population estimation

Summary Multi-stage sampling is a convenient technique suited to the desnity estimation of biological populations living in habitats with complicated structures. This paper describes a general method of its application to population estimation in which the preliminary information on the spatial distribution pattern of the population under study can be incorporated as the parameters of the mean crowding-mean relationship. The formulae that are necessary to perform sequential or double sampling plans for its efficient application are derived. The procedure of application of the method is explained with a numerical example. This study was supported by science research fund from the Ministry of Education.     

A suggestion for computing objective function in model calibration

A parameter-optimization process (model calibration) is usually required for numerical model applications, which involves the use of an objective function to determine the model cost (model-data errors). The sum of square errors (SSR) has been widely adopted as the objective function in various optimization procedures. However, ‘square error’ calculation was found to be more sensitive to extreme or high values. Thus, we proposed that the sum of absolute errors (SAR) may be a better option than SSR for model calibration. To test this hypothesis, we used two case studies—a hydrological model calibration and a biogeochemical model calibration—to investigate the behavior of a group of potential objective functions: SSR, SAR, sum of squared relative deviation (SSRD), and sum of absolute relative deviation (SARD). Mathematical evaluation of model performance demonstrates that ‘absolute error’ (SAR and SARD) are superior to ‘square error’ (SSR and SSRD) in calculating objective function for model calibration, and SAR behaved the best (with the least error and highest efficiency). This study suggests that SSR might be overly used in real applications, and SAR may be a reasonable choice in common optimization implementations without emphasizing either high or low values (e.g., modeling for supporting resources management).     

Dosimetric assessment of an exposure system for simulating GSM and WCDMA mobile phone usage

An exposure system for investigation of volunteers during simulated GSM and WCDMA mobile phone usage has been designed. The apparatus consists of a dual band antenna with enhanced carrying properties that enables exposure for at least 8 h a day. For GSM a 900 MHz pulse modulated carrier was used. The QPSK modulated WCDMA signal at 1966 MHz comprises a power control scheme, which was designed for investigations of biological effects. The dosimetry of the exposure system by measurements and calculations is described in detail within this paper. It is shown that the SAR distribution of the antenna shows similar characteristics to mobile phones with an integrated antenna. The 10 g averaged localized SAR, normalized to an antenna input power of 1 W and measured in the flat phantom area of the SAM phantom, amounts to 7.82 mW/g (900 MHz) and 10.98 mW/g (1966 MHz). The simulated SAR(10 g) in the Visible Human head model agrees with measured values to within 20%. A variation of the antenna rotation angle results in an SAR(10 g) change below 17%. The increase of the antenna distance by 2 mm with respect to the human head leads to an SAR(10 g) change of 9%.     

Empirical validation of SAR values predicted by FDTD modeling.

Rapid increase in the use of numerical techniques to predict current density or specific absorption rate (SAR) in sophisticated three dimensional anatomical computer models of man and animals has resulted in the need to understand how numerical solutions of the complex electrodynamics equations match with empirical measurements. This aspect is particularly important because different numerical codes and computer models are used in research settings as a guide in designing clinical devices, telecommunication systems, and safety standards. To ensure compliance with safety guidelines during equipment design, manufacturing and maintenance, realistic and accurate models could be used as a bridge between empirical data and actual exposure conditions. Before these tools are transitioned into the hands of health safety officers and system designers, their accuracy and limitations must be verified under a variety of exposure conditions using available analytical and empirical dosimetry techniques. In this paper, empirical validation of SAR values predicted by finite difference time domain (FDTD) numerical code on sphere and rat is presented. The results of this study show a good agreement between empirical and theoretical methods and, thus, offer a relatively high confidence in SAR predictions obtained from digital anatomical models based on the FDTD numerical code.     

Quantitative characters under assortative mating: Gametic model

The gametic model introduced by Gimelfarb (1982, Theor. Pop. Biol. 22, 324-366) is applied to investigating the dynamics, represented in the model by a second-order recurrence equation, the the variance of sex-independent and sex-controlled characters under assortative mating. It is shown that, for any additive character, there always exists a unique equilibrium for the variance, which is stable. Dynamical properties of the variance under positive and negative matings are considered, and numerical evaluations of the equilibrium values as well as of the dynamical changes of the variance are presented. Comparisons with results from a biological experiment are made.     

Mobile phone electromagnetic radiation activates MAPK signaling and regulates viability in Drosophila

Mobile phones are widely used in the modern world. However, biological effects of electromagnetic radiation produced by mobile phones are largely unknown. In this report, we show biological effects of the mobile phone 835 MHz electromagnetic field (EMF) in the Drosophila model system. When flies were exposed to the specific absorption rate (SAR) 1.6 W/kg, which is the proposed exposure limit by the American National Standards Institute (ANSI), more than 90% of the flies were viable even after the 30 h exposure. However, in the SAR 4.0 W/kg strong EMF exposure, viability dropped from the 12 h exposure. These EMF exposures triggered stress response and increased the production of reactive oxygen species. The EMF exposures also activated extracellular signal regulated kinase (ERK) and c-Jun N-terminal kinase (JNK) signaling, but not p38 kinase signaling. Interestingly, SAR 1.6 W/kg activated mainly ERK signaling and expression of an anti-apoptotic gene, whereas SAR 4.0 W/kg strongly activated JNK signaling and expression of apoptotic genes. In addition, SAR 4.0 W/kg amplified the number of apoptotic cells in the fly brain. These findings demonstrate that the exposure limit on electromagnetic radiation proposed by ANSI triggered ERK-survival signaling but the strong electromagnetic radiation activated JNK-apoptotic signaling in Drosophila.     

Specific absorption rate in electrically coupled biological samples between metal plates

The specific absorption rate (SAR) in a biological sample irradiated by electromagnetic fields between the metal plates of a transmission line can be altered significantly by the spacing of the metal plates and the distance between neighboring samples. The SAR in spherical biological samples is calculated for a number of neighboring sample arrangements and metal-plate spacings by using the method of images and induced dipole coupling. For a decrease in metal-plate spacing, the derived equations predict an increase in SAR within a sample and a decrease in SAR with a decrease in neighboring-sample spacing. The calculations are compared with measurements made with the aid of an array of 1-in radius metal hemispheres on the lower plate of two parallel plates (thus forming an image system). The hemisphere on which measurements are taken is insulated from the metal plate and is connected via a coaxial center conductor to an HP 3582A spectrum analyzer that measures the voltage and hence the electric field intensity at the hemisphere. Measurements made at a frequency where wavelength is large compared with sample size (48 Hz) are in good agreement with calculations.     

Applying Methods from Differential Geometry to Devise Stable and Persistent Air Layers Attached to Objects Immersed in Water

We describe a few mathematical tools which allow to investigate whether air-water interfaces exist(under prescribedconditions)and are mechanically stable and temporally persistent.In terms of physics,air-water interfaces are governed by theYoung-Laplace equation.Mathematically they are surfaces of constant mean curvature which represent solutions of a nonlinearelliptic partial differential equation.Although explicit solutions of this equation can be obtained only in very special cases,it is-under moderately special circumstances-possible to establish the existence of a solution without actually solving thedifferential equation.We also derive criteria for mechanical stability and temporal persistence of an air layer.Furthermorewe calculate the lifetime of a non-persistent air layer.Finally,we apply these tools to two examples which exhibit the symmetriesof 2D lattices.These examples can be viewed as abstractions of the biological model represented by the aquatic fernSalvinia.     

Nonlinear control for algae growth models in the chemostat

This paper deals with output feedback control of phytoplanktonic algae growth models in the chemostat. The considered class of model is of variable yield type, meaning that the ratio between the environmental nutrient absorption rate and the cells’ growth rate varies, which is different from classical bioprocesses assumptions. On the basis of weak qualitative hypotheses on the analytical expressions of the involved biological phenomena (which guarantee robustness of the procedure toward modeling uncertainties) we propose a nonlinear controller and prove its ability to globally stabilize such processes. Finally, we illustrate our approach with numerical simulations and show its benefits for biological laboratory experiments, especially for ensuring persistence of the culture facing classical experimental problems.