Magnetic induction at 60 Hz in the human heart: a comparison between the in situ and isolated scenarios

Numerical modelling is used to estimate the electric fields and currents induced in the human heart and associated major blood vessels by 60 Hz external magnetic fields. The modelling is accomplished using a scalar-potential finite-difference code applied to a 3.6-mm resolution voxel-based model of the whole human body. The main goal of the present work is a comparison between the induced field levels in the heart located in situ and in isolation. This information is of value in assessing any health risks due to such fields, given that some existing protection standards consider the heart as an isolated conducting body. It is shown that the field levels differ significantly between these two scenarios. Consequently, data from more realistic and detailed numerical studies are required for the development of reliable standards.     

Finite element modelling approaches for well-ordered porous metallic materials for orthopaedic applications: cost effectiveness and geometrical considerations

The mechanical properties of well-ordered porous materials are related to their geometrical parameters at the mesoscale. Finite element (FE) analysis is a powerful tool to design well-ordered porous materials by analysing the mechanical behaviour. However, FE models are often computationally expensive. This article aims to develop a cost-effective FE model to simulate well-ordered porous metallic materials for orthopaedic applications. Solid and beam FE modelling approaches are compared, using finite size and infinite media models considering cubic unit cell geometry. The model is then applied to compare two unit cell geometries: cubic and diamond. Models having finite size provide similar results than the infinite media model approach for large sample sizes. In addition, these finite size models also capture the influence of the boundary conditions on the mechanical response for small sample sizes. The beam FE modelling approach showed little computational cost and similar results to the solid FE modelling approach. Diamond unit cell geometry appeared to be more suitable for orthopaedic applications than the cubic unit cell geometry.     

Image resolution enhancement using statistical estimation in wavelet domain

The goal of medical image resolution enhancement is to reconstruct a higher-resolution image from its lower-resolution counterpart. This paper proposes a Bayesian approach in the wavelet domain by exploiting a Bayesian inference framework to mathematically formulate the image interpolation problem. Furthermore, the proposed approach jointly estimates both the unknown wavelet coefficients of the high-resolution image and the unknown parameters of the statistical model for wavelet coefficients. Experiments are conducted to demonstrate the superior performance of the proposed approach.     

Currents induced in anatomic models of the human for uniform and nonuniform power frequency magnetic fields

We have used the quasi-static impedance method to calculate the currents induced in the nominal 2 x 2 x 3 and 6 mm resolution anatomically based models of the human body for exposure to magnetic fields at 60 Hz. Uniform magnetic fields of various orientations and magnitudes 1 or 0.417 mT suggested in the ACGIH and ICNIRP safety guidelines are used to calculate induced electric fields or current densities for the various glands and organs of the body including the pineal gland. The maximum 1 cm(2) area-averaged induced current densities for the central nervous system tissues, such as the brain and the spinal cord, were within the reference level of 10 mA/m(2) as suggested in the ICNIRP guidelines for magnetic fields (0.417 mT at 60 Hz). Tissue conductivities were found to play an important role and higher assumed tissue conductivities gave higher induced current densities. We have also determined the induced current density distributions for nonuniform magnetic fields associated with two commonly used electrical appliances, namely a hair dryer and a hair clipper. Because of considerably higher magnetic fields for the latter device, higher induced electric fields and current densities were calculated.     

Bone Load Estimation for the Proximal Femur Using Single Energy Quantitative CT Data

A density-based load estimation method was applied to determine femoral load patterns. Two-dimensional finite element models were constructed using single energy quantitative computed tomography (QCT) data from two femora. Basic load cases included parabolic pressure joint loads and constant tractions on the greater trochanter. An optimization procedure adjusted magnitudes of the basic load cases, such that the applied mechanical stimulus approached the ideal stimulus throughout each model. Dominant estimated load directions were generally consistent with published experimental data for gait. Other estimated loads suggested that loads at extreme joint orientations may be important to maintenance of bone structure. Remodeling simulations with the estimated loads produced density distributions qualitatively similar to the QCT data sets. Average nodal density errors between QCT data and predictions were 0.24 g/cm(3) and 0.28 g/cm(3). The results indicate that density-based load estimation could improve understanding of loading patterns on bones.     

The influence of local tissue conductivity changes on the magnetoencephalogram and the electroencephalogram.

We examined the influence of local tissue conductivity changes in the vicinity of a dipolar source on the neuromagnetic field and the electric scalp potential using a high resolution finite element method model of the human head. We found that the topology of both the electric scalp potential and the neuromagnetic field (and consequently dipole localization) is influenced significantly by conductivity changes only in voxels adjacent to the source. Conductivity changes in these voxels yield a greater change in the amplitude of the magnetic field (and consequently in the dipole strength) than in the amplitude of the electric potential.     

Comparison of patella bone strain between females with and without patellofemoral pain: A finite element analysis study

Elevated bone principal strain (an indicator of potential bone injury) resulting from reduced cartilage thickness has been suggested to contribute to patellofemoral symptoms. However, research linking patella bone strain, articular cartilage thickness, and patellofemoral pain (PFP) remains limited. The primary purpose was to determine whether females with PFP exhibit elevated patella bone strain when compared to pain-free controls. A secondary objective was to determine the influence of patella cartilage thickness on patella bone strain. Ten females with PFP and 10 gender, age, and activity-matched pain-free controls participated. Patella bone strain fields were quantified utilizing subject-specific finite element (FE) models of the patellofemoral joint (PFJ). Input parameters for the FE model included (1) PFJ geometry, (2) elastic moduli of the patella bone, (3) weight-bearing PFJ kinematics, and (4) quadriceps muscle forces. Using quasi-static simulations, peak and average minimum principal strains as well as peak and average maximum principal strains were quantified. Cartilage thickness was quantified by computing the perpendicular distance between opposing voxels defining the cartilage edges on axial plane magnetic resonance images. Compared to the pain-free controls, individuals with PFP exhibited increased peak and average minimum and maximum principal strain magnitudes in the patella. Additionally, patella cartilage thickness was negatively associated with peak minimum principal patella strain and peak maximum principal patella strain. The elevated bone strain magnitudes resulting from reduced cartilage thickness may contribute to patellofemoral symptoms and bone injury in persons with PFP.     

General properties of the interaction between animals and ELF electric fields

An analysis is given of the interaction between extremely low-frequency (ELF) electric fields and animals of arbitrary body shape. This analysis is based on three approximations which are valid in the ELF range: In living tissues, capacitive (displacement) currents are negligible compared to conduction currents; effects resulting from the finite velocity of propagation of electromagnetic fields are negligible; skin effect in living tissues is negligible. Major conclusions of the analysis are: (a) The electric field outside the body, the induced charge on the surface of the body, and the total current crossing any section through the body (eg, through the neck or limbs) are completely determined by the characteristics of the applied ELF electric field, the shape of the body, its location relative to ground and other conductors, and any conduction currents from the body to ground or other conductors. (b) All of the quantities in (a) can be measured using conducting animal models. (c) The magnitudes of the electric field outside the body and the induced charge density on the surface of the body are independent of frequency, in the ELF range, when the body is either insulated from or shorted to ground (and any other conductors in the system). (d) The only quantities affected by the electrical properties of the tissues comprising the body are the current density and electric field inside the body. (e) The electric field outside and inside a body will be unchanged by a scaled change in its size.     

Bone Load Estimation for the Proximal Femur Using Single Energy Quantitative CT Data

A density-based load estimation method was applied to determine femoral load patterns. Two-dimensional finite element models were constructed using single energy quantitative computed tomography (QCT) data from two femora. basic load cases included parabolic pressure joint loads and constant tractions on the greater trochanter. An optimization procedure adjusted magnitudes of the basic load cases, such that the applied mechanical stimulus approached the ideal stimulus throughout each model. Dominant estimated load directions were generally consistent with published experimental data for gait. Other estimated loads suggested that loads at extreme joint orientations may be important to maintenance of bone structure. Remodeling simulations with the estimated loads produced density distributions qualitatively similar to the QCT data sets. Average nodal density errors between QCT data and predictions were 0·24 g/cm³ and 0·28 g/cm³. The results indicate that density-based load estimation could improve understanding of loading patterns on bones.     

Proximal Femoral Density Patterns are Consistent with Bicentric Joint Loads

We developed an alternate method for density-based load estimation and applied it to estimate hip joint load distributions for two femora. Two-dimensional finite element models were constructed from single energy quantitative computed tomography (QCT) data. Load estimation was performed using five loading regions on the femoral head. Within each loading region, individual nodal loads, normal to the local surface, were supplied as input to the load estimation. An optimization procedure independently adjusted individual nodal load magnitudes in each region, and the magnitudes of muscle forces on the greater trochanter, such that the applied tissue stimulus approached the reference stimulus throughout the model. Dominant estimated load resultant directions were generally consistent with published experimental data for loads during gait. The estimated loads also suggested that loads near the extremes of the articulating surface may be important (even required) for development and maintenance of normal bone architecture. Estimated load distributions within nearly all regions predicted bicentric loading patterns, which are consistent with observations of hip joint incongruity. Remodeling simulations with the estimated loads predicted density distributions with features qualitatively similar to the QCT data sets. This study illustrates how applications of density-based bone load estimation can improve understanding of dominant loading patterns in other bones and joints. The prediction of bicentric loading suggests a very fine level of local adaptation to details of joint loading.     

Comparison of cardiac and 60 Hz magnetically induced electric fields measured in anesthetized rats

Extremely low frequency magnetic fields interact with an animal by inducing internal electric fields, which are in addition to the normal endogenous fields present in living animals. Male rats weighing about 560 g each were anesthetized with ketamine and xylazine. Small incisions were made in the ventral body wall at the chest and upper abdomen to position a miniature probe for measuring internal electric fields. The calibration constant for the probe size was 5.7 mm, with a flat response from at least 12 Hz to 20 kHz. A cardiac signal, similar to the normal electrocardiogram with a heart rate of about 250 bpm, was readily obtained at the chest. Upon analysis of its spectrum, the cardiac field detected by the probe had a broad maximum at 32–95 Hz. When the rats were exposed to a 1 mT, 60 Hz magnetic field, a spike appeared in the spectrum at 60 Hz. The peak-to-peak magnitudes of electric fields associated with normal heart function were comparable to fields induced by a 1 mT magnetic field at 60 Hz for those positions measured on the body surface (where induced fields were maximal). Within the body, or in different directions relative to the applied field, the induced fields were reduced (reaching zero at the center of the animal). The cardiac field increased near the heart, becoming much larger than the induced field. Thus, the cardiac electric field, together with the other endogenous fields, combine with induced electric fields and help to provide reference levels for the induced-field dosimetry of ELF magnetic field exposures of living animals. Bioelectromagnetics 18:317–323, 1997. © 1997 Wiley-Liss, Inc.     

Proximal Femoral Density Patterns are Consistent with Bicentric Joint Loads

We developed an alternate method for density-based load estimation and applied it to estimate hip joint load distributions for two femora. Two-dimensional finite element models were constructed from single energy quantitative computed tomography (QCT) data. Load estimation was performed using five loading regions on the femoral head. Within each loading region, individual nodal loads, normal to the local surface, were supplied as input to the load estimation. An optimization procedure independently adjusted individual nodal load magnitudes in each region, and the magnitudes of muscle forces on the greater trochanter, such that the applied tissue stimulus approached the reference stimulus throughout the model. Dominant estimated load resultant directions were generally consistent with published experimental data for loads during gait. The estimated loads also suggested that loads near the extremes of the articulating surface may be important (even required) for development and maintenance of normal bone architecture. Estimated load distributions within nearly all regions predicted bicentric loading patterns, which are consistent with observations of hip joint incongruity. Remodeling simulations with the estimated loads predicted density distributions with features qualitatively similar to the QCT data sets. This study illustrates how applications of density-based bone load estimation can improve understanding of dominant loading patterns in other bones and joints. The prediction of bicentric loading suggests a very fine level of local adaptation to details of joint loading.     

Cell culture dosimetry for low-frequency magnetic fields

Calculations of the current density and electric field distributions induced in cell cultures by an applied low-frequency magnetic field have assumed that the medium is uniform. This paper calculates these distributions for a more realistic, inhomogeneous, anisotropic model in which the cells are regarded as conducting squares surrounded by insulating membranes. Separate parameters are used to specify the resistivities of the cell interior, the cell membrane parallel to its surface, the cell membrane perpendicular to its surface, and the intercellular junction parallel to the membrane. The presence of gap junctions connecting the interiors of adjacent cells is also considered. For vertical applied magnetic fields, the induced currents and field distributions may deviate considerably from the homogeneous medium model if there is sufficiently tight binding of the cells to each other. The presence of gap junctions can produce relatively large transmembrane electric fields or intracellular current densities. These considerations are generally less important for horizontal applied fields. A simple microscopic model of the cell surface is also discussed. © 1996 Wiley-Liss, Inc.     

Vertical circularly polarized ELF magnetic fields and induced electric fields in culture media

Some properties of induced electric fields in cell culture media produced by vertical circularly polarized magnetic fields are examined. The described geometry is not advantageous for determining effects that may be attributable to induced electric fields or currents. Bioelectromagnetics 18:524–526, 1997. Published 1997 Wiley-Liss, Inc.     

An elastic network model based on the structure of the red blood cell membrane skeleton.

A finite element network model has been developed to predict the macroscopic elastic shear modulus and the area expansion modulus of the red blood cell (RBC) membrane skeleton on the basis of its microstructure. The topological organization of connections between spectrin molecules is represented by the edges of a random Delaunay triangulation, and the elasticity of an individual spectrin molecule is represented by the spring constant, K, for a linear spring element. The model network is subjected to deformations by prescribing nodal displacements on the boundary. The positions of internal nodes are computed by the finite element program. The average response of the network is used to compute the shear modulus (mu) and area expansion modulus (kappa) for the corresponding effective continuum. For networks with a moderate degree of randomness, this model predicts mu/K = 0.45 and kappa/K = 0.90 in small deformations. These results are consistent with previous computational models and experimental estimates of the ratio mu/kappa. This model also predicts that the elastic moduli vary by 20% or more in networks with varying degrees of randomness. In large deformations, mu increases as a cubic function of the extension ratio lambda 1, with mu/K = 0.62 when lambda 1 = 1.5.     

Evaluation and characterization of fetal exposures to low frequency magnetic fields generated by laptop computers

Portable – or “laptop” – computers (LCs) are widely and increasingly used all over the world. Since LCs are often used in tight contact with the body even by pregnant women, fetal exposures to low frequency magnetic fields generated by these units can occur. LC emissions are usually characterized by complex waveforms and are often generated by the main AC power supply (when connected) and by the display power supply sub-system.In the present study, low frequency magnetic field emissions were measured for a set of five models of portable computers. For each of them, the magnetic flux density was characterized in terms not just of field amplitude, but also of the so called “weighted peak” (WP) index, introduced in the 2003 ICNIRP Statement on complex waveforms and confirmed in the 2010 ICNIRP Guidelines for low frequency fields. For the model of LC presenting the higher emission, a deeper analysis was also carried out, using numerical dosimetry techniques to calculate internal quantities (current density and in-situ electric field) with reference to a digital body model of a pregnant woman. Since internal quantities have complex waveforms too, the concept of WP index was extended to them, considering the ICNIRP basic restrictions defined in the 1998 Guidelines for the current density and in the 2010 Guidelines for the in-situ electric field. Induced quantities and WP indexes were computed using an appropriate original formulation of the well known Scalar Potential Finite Difference (SPFD) numerical method for electromagnetic dosimetry in quasi-static conditions.     

Microsystem for transfection of exogenous molecules with spatio-temporal control into adherent cells

Several non-viral techniques involving the use of liposomes, particle bombardment and electroporation have been used for efficient transfection of plasmids and other molecules into cells. Current approaches target whole or bulk regions of tissue, lacking the desired spatial control over the transfection process. In this study, we present a novel approach using microsystems to achieve spatial and temporal control over the transfection process in adherent cells. A 6x6 MEA (microelectrode array) with 100 microm microelectrode dimension was developed on a silicon substrate using standard microfabrication procedures and passivated with a biocompatible layer. Using finite element models, electric field intensities were simulated and locations of optimal electroporation zones in the cell culture on the microelectrode surface were predicted. The MEA was subsequently tested using 3T3 fibroblasts cultured on the MEA surface for 96 h and stimulation voltages in the range of 2-5 V in the presence of propidium iodide (PI), a cell impermeant dye. Maximum electric field intensities in the z-direction were estimated to be in the range of 320-820 V/cm for applied differential voltages in the range of 2-5 V. Cells directly on the top and on the edges of the stimulating microelectrodes in the MEA were preferentially transfected with PI as predicted by the simulations. The results of these experiments demonstrate that spatial and temporal control of desired regions of transfection in vitro can be achieved using MEAs and electroporation.     

Peripheral electrosense physiology: a review of recent findings.

Advances, since 1974, in understanding the physiology of electroreceptors are reviewed. In brief: 1. In fish that produce a weak electric discharge with electric organs, the tuberous electroreceptors are generally most sensitive to stimulus frequencies near the species', individual's, and even local, waveform of the electric organ discharge; there is a good match between receptor sensitivity and the normal stimulus. 2. The ability of tuberous electroreceptors to detect field distortions produced by reasonably sized objects is limited; an object must be closer than a body-length to be detected, and the afferent response is a negative power function of object distance. 3. The second major electroreceptor class, the ampullary electroreceptors, is sensitive to low frequency, low intensity electric fields, and this acute sensitivity results in the ability of the receptors in marine species to detect magnetic fields on the order of the Earth's. 4. The calcium ion is essential for normal functioning of ampullary electroreceptors.     

A new method for the simulation of electric fields,generated by electric fish,and their distorsions by objects

Among the many species of fishes endowed with electric organs Mormyriformes and Gymnotoidei are known to emit and receive electric signals for the purposes of intraspecific communication and recognition of objects. Models which have been proposed for this electro-sensory system generally assume steady-state conditions. On the other hand, the very character of the signals itself and the idea that the cerebellum might be working as a clock point to the importance of the signal dynamics. Therefore a new approach to the simulation of electric fields is described in the paper. The basic idea is to superpose the fields of point charges in a way that the sum is in accordance with the fish's electric field. The same technique could be used to simulate the influence of objects on the electric field. Following a suggestion of Dr. E. Kasper I used a simpler but equal effective approach for object simulation consisting in the use of a dipole instead of point charges. The model described is easily applied to diverse situations and allows one to estimate the influence of various parameters (size, shape, and position) on the “electric image” of an object. Furthermore, the well-known behaviour of tailbending and its consequences in object recognition can be simulated. The results underline the importance of signal dynamics for species with pulse-type discharges.