Pulsatile flow of blood through a stenosed tube: effect of periodic body acceleration and a magnetic field

A proper understanding of the interactions of body acceleration and a magnetic field with blood flow could be useful in the diagnosis and treatment of some health problems. In the work reported in this paper we studied the pulsatile flow of blood through stenosed arteries, including the effects of body acceleration and a magnetic field. Blood is regarded as an electrically conducting, incompressible, couple-stress fluid in the presence of a magnetic field along the radius of the tube. The effects of the body acceleration and the magnetic field on the axial velocity, flow rate, and fluid acceleration were obtained analytically by use of the Hankel transform and the Laplace transform. Velocity variations under different conditions are shown graphically. The results have been compared with those from other theoretical models, and are in good agreement. Finally, our mathematical model gives a simple velocity expression for blood flow so it will help not only in the field of physiological fluid dynamics but will also help medical practitioners with elementary knowledge of mathematics.     

3D Magnetic Holes in Collisionless Plasmas

Recent multispacecraft observations in the Earth’s magnetosphere have revealed an abundance of magnetic holes—localized magnetic field depressions. These magnetic holes are characterized by the plasma pressure enhancement and strongly localized currents flowing around the hole boundaries. There are several numerical and analytical models describing 2D configurations of magnetic holes, but the 3D distribution of magnetic fields and electric currents is studied poorly. Such a 3D magnetic field configuration is important for accurate investigation of charged particle dynamics within magnetic holes. Moreover, the 3D distribution of currents can be used for distant probing of magnetic holes in the magnetosphere. In this study, a 3D magnetic hole model using the single-fluid approximation and a spatial scale hierarchy with the distinct separation of gradients is developed. It is shown that such 3D holes can be obtained as a generalization of 1D models with the plasma pressure distribution adopted from the kinetic approach. The proposed model contains two magnetic field components and field-aligned currents. The magnetic field line configuration resembles the magnetic trap where hot charged particles bounce between mirror points. However, the approximation of isotropic pressure results in a constant plasma pressure along magnetic field lines, and the proposed magnetic hole model does not confine plasma along the field direction.     

Formation of electrode sheaths during the acceleration of a magnetized plasma

A study is made of the motion of a plasma with a frozen-in magnetic field along the electrode surfaces in the direction transverse to the magnetic field. A one-dimensional problem of an electrode sheath is formulated in which all of the quantities depend only on the coordinate orthogonal to the electrode surface. Viscous plasma heating, plasma cooling via heat conduction, and other kinetic effects are taken into consideration. Account is also taken of the effect of plasma acceleration and of the related current that is transverse to the electrode surfaces and, due to the Hall effect, carries the magnetic flux away from the cathode and toward the anode. Solving the one-dimensional problem with a constant electric current and constant magnetic field shows that, in a sheath that forms near the cathode, the solution becomes self-similar, the plasma mass grows linearly, and the electron magnetization parameter remains unchanged. It is found that the anode sheath cannot be described in the magnetohydrodynamic approximation, according to which the plasma density in the sheath rapidly vanishes, while the current through the sheath remains constant. This difficulty can be overcome by incorporating some of the nonhydrodynamic effects (primarily, electron dispersion), thereby making the problem physically correct. Solving the problem numerically shows that a decrease in the plasma density in the anode sheath due to the Hall effect gives rise to additional significant plasma acceleration.     

Brain stimulation using electromagnetic sources: theoretical aspects.

We prove that, at the frequencies generally proposed for extracranial stimulation of the brain, it is not possible, using any superposition of external current sources, to produce a three-dimensional local maximum of the electric field strength inside the brain. The maximum always occurs on a boundary where the conductivity jumps in value. Nevertheless, it may be possible to achieve greater two-dimensional focusing and shaping of the electric field than is currently available. Towards this goal we have used the reciprocity theorem to present a uniform treatment of the electric field inside a conducting medium produced by a variety of sources: an external magnetic dipole (current loop), an external electric dipole (linear antenna), and surface and depth electrodes. This formulation makes use of the lead fields from magneto- and electroencephalography. For the special case of a system with spherically symmetric conductivity, we derive a simple analytic formula for the electric field due to an external magnetic dipole. This formula is independent of the conductivity profile and therefore embraces spherical models with any number of shells. This explains the "insensitivity" to the skull's conductivity that has been described in numerical studies. We also present analytic formulas for the electric field due to an electric dipole, and also surface and depth electrodes, for the case of a sphere of constant conductivity.     

Reduced Efficiency of Magnetotaxis in Magnetotactic Coccoid Bacteria in Higher than Geomagnetic Fields

Magnetotactic bacteria are microorganisms that orient and migrate along magnetic field lines. The classical model of polar magnetotaxis predicts that the field-parallel migration velocity of magnetotactic bacteria increases monotonically with the strength of an applied magnetic field. We here test this model experimentally on magnetotactic coccoid bacteria that swim along helical trajectories. It turns out that the contribution of the field-parallel migration velocity decreases with increasing field strength from 0.1 to 1.5 mT. This unexpected observation can be explained and reproduced in a mathematical model under the assumption that the magnetosome chain is inclined with respect to the flagellar propulsion axis. The magnetic disadvantage, however, becomes apparent only in stronger than geomagnetic fields, which suggests that magnetotaxis is optimized under geomagnetic field conditions. It is therefore not beneficial for these bacteria to increase their intracellular magnetic dipole moment beyond the value needed to overcome Brownian motion in geomagnetic field conditions.     

Simulation of two-dimensional fully developed laminar flow for a magneto-hydrodynamic (MHD) pump

MHD micro-pumps circumvent the wear and fatigue caused by high pressure-drop across the check valves of mechanical micro-pumps in micro-fluidic systems. Early analyses of the fluid flow for MHD micro-pumps were mostly made possible by the Poiseuille flow theory; however, this conventional laminar approach cannot illustrate the effects of various channel sizes and shapes. This paper, therefore, presents a simplified MHD flow model based upon steady state, incompressible and fully developed laminar flow theory to investigate the characteristics of a MHD pump. Inside the pump, flowing along the channel is the electrically conducting fluid flowing driven by the Lorentz forces in the direction perpendicular to both dc magnetic field and applied electric currents. The Lorentz forces were converted into a hydrostatic pressure gradient in the momentum equations of the MHD channel flow model. The numerical simulations conducted with the explicit finite difference method show that the channel dimensions and the induced Lorentz forces have significant influences on the flow velocity profile. Furthermore, the simulation results agree well with the experimental results published by other researchers.     

Magnetic stimulation of one-dimensional neuronal cultures

Transcranial magnetic stimulation is a remarkable tool for neuroscience research, with a multitude of diagnostic and therapeutic applications. Surprisingly, application of the same magnetic stimulation directly to neurons that are dissected from the brain and grown in vitro was not reported to activate them to date. Here we report that central nervous system neurons patterned on large enough one-dimensional rings can be magnetically stimulated in vitro. In contrast, two-dimensional cultures with comparable size do not respond to excitation. This happens because the one-dimensional pattern enforces an ordering of the axons along the ring, which is designed to follow the lines of the magnetically induced electric field. A small group of sensitive (i.e., initiating) neurons respond even when the network is disconnected, and are presumed to excite the entire network when it is connected. This implies that morphological and electrophysiological properties of single neurons are crucial for magnetic stimulation. We conjecture that the existence of a select group of neurons with higher sensitivity may occur in the brain in vivo as well, with consequences for transcranial magnetic stimulation.     

Coronary heart diseases: Assessment of risk associated with work exposure to ultralow-frequency magnetic fields

The present analysis was stimulated by previous findings on the possible influence of natural ultralow-frequency (ULF; 0.001–10 Hz) geomagnetic field variations on the cardiovascular system and indications of an effect of man-made ULF magnetic fields on the rate of myocardial infarction. In the present study, we considered the occupational health hazards of the strongest ULF magnetic fields in densely populated urban areas. Measurements of ULF magnetic field fluctuations produced by trains powered by DC electricity were performed by means of a computer-based, highly sensitive, three-component magnetometer. We found that the magnitude of magnetic field pulses inside the driver's cab of electric locomotives (ELs) could be ≥ 280 μT in the horizontal component perpendicular to the rails and up to approximately 130 μT in the vertical component, and, in the driver's compartment of electric motor unit (EMU) trains, they were approximately 50 and 35 μT, respectively. We have investigated the relationships between the occupational exposure to ULF magnetic field fluctuations produced by electric trains and cardiovascular diseases (CVDs) among railroad workers in the former Soviet Union. We have analyzed medical statistical data for a period of 3 years for approximately 45,000 railroad workers and 4,000 engine drivers. We have also analyzed 3 years of morbidity data for three subgroups of engine drivers (∼4,000 in each group) operating different types of trains. We find that EL drivers have a twofold increase in risk (2.00 ± 0.27) of coronary heart diseases (CHDs) compared with EMU drivers. Because our analysis of major CVDs shows that the examined subpopulations of drivers can be considered to have had equal exposure to all known risk factors, the elevated CHD risk among EL drivers could be attributed to the increased occupational exposure to ULF magnetic fields. © 1996 Wiley-Liss, Inc.     

Optically pumped magnetometers disclose magnetic field components of the muscular action potential

AimAiming at analysing the signal conduction in muscular fibres, the spatio-temporal dynamics of the magnetic field generated by the propagating muscle action potential (MAP) is studied.MethodIn this prospective, proof of principle study, the magnetic activity of the intrinsic foot muscle after electric stimulation of the tibial nerve was measured using optically pumped magnetometers (OPMs). A classical biophysical electric dipole model of the propagating MAP was implemented to model the source of the data. In order to account for radial currents of the muscular tubules system, a magnetic dipole oriented along the direction of the muscle was added.ResultsThe signal profile generated by the activity of the intrinsic foot muscles was measured by four OPM devices. Three OPM sensors captured the spatio-temporal magnetic field pattern of the longitudinal intrinsic foot muscles. Changes of the activation pattern reflected the propagating muscular action potential along the muscle. A combined electric and magnetic dipole model could explain the recorded magnetic activity.InterpretationOPM devices allow for a new, non-invasive way to study MAP patterns. Since magnetic fields are less altered by the tissue surrounding the dipole source compared to electric activity, a precise analysis of the spatial characteristics and temporal dynamics of the MAP is possible. The classic electric dipole model explains major but not all aspects of the magnetic field. The field has longitudinal components generated by intrinsic structures of the muscle fibre. By understanding these magnetic components, new methods could be developed to analyse the muscular signal transduction pathway in greater detail. The approach has the potential to become a promising diagnostic tool in peripheral neurological motor impairments.     

可描述横向电场中外周神经兴奋的电缆方程

传统的电缆方程只能用于描述纵向电场中外周神经的兴奋,无法描述外周神经在横向电场作用下的兴奋,其于两阶段过程模型,提出一种改进的电缆方程,可以描述外周神经在横向电场中的兴奋,其结果和Struijk的离体实验数据相吻合。此改进的电缆方程可用于描述任意电场中外周神经的兴奋。     

MHD Free Convective Boundary Layer Flow of a Nanofluid past a Flat Vertical Plate with Newtonian Heating Boundary Condition

Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.     

Magnetic alignment in warthogs Phacochoerus africanus and wild boars Sus scrofa

Magnetic alignment (MA) results from the preference of animals to align themselves along the field lines of the geomagnetic field, a behavioural expression of a magnetic sense. MA is well documented for ruminants and might demonstrate a general magnetic sensory ability among artiodactyls. We measured body‐axis alignment in 1614 foraging or resting wild boars Sus scrofa, 1849 wild boar beds, and 1347 warthogs Phacochoerus africanus, and found a highly significant north–south preference. The magnetic field was the only common denominator of all observations. Thus, we provide the first data suggesting a magnetic sense in the Suidae.     

Convergence to the island-model coalescent process in populations with restricted migration

In this article we apply some graph-theoretic results to the study of coalescence in a structured population with migration. The graph is the pattern of migration among subpopulations, or demes, and we use the theory of random walks on graphs to characterize the ease with which ancestral lineages can traverse the habitat in a series of migration events. We identify conditions under which the coalescent process in populations with restricted migration, such that individuals cannot traverse the habitat freely in a single migration event, nonetheless becomes identical to the coalescent process in the island migration model in the limit as the number of demes tends to infinity. Specifically, we first note that a sequence of symmetric graphs with Diaconis-Stroock constant bounded above has an unstructured Kingman-type coalescent in the limit for a sample of size two from two different demes. We then show that circular and toroidal models with long-range but restricted migration have an upper bound on this constant and so have an unstructured-migration coalescent in the limit. We investigate the rate of convergence to this limit using simulations.     

Separation of the heavy and light ion components in a plasma flow propagating in a curvilinear magnetic field

The propagation of a metal plasma jet in a transport system with a curvilinear magnetic field was studied experimentally. The jet was generated by a pulsed vacuum arc discharge with a composite (W + Fe) cathode. Spatial separation of ions of the cathode material was observed at the exit from the system. The ions of the lighter element (Fe) were concentrated in the inner part of the cathode plasma jet deflected by the magnetic field. The jet is also found to be deflected along the binormal to the magnetic field lines due to plasma drift in the crossed magnetic and electric fields. The degree of mass separation of elements is shown to increase with increasing jet deflection along the binormal. The maximum value of the mass separation efficiency reaches 45, the effective value being 7.7.     

Comparison of coupling of humans to electric and magnetic fields with frequencies between 100 Hz and 100 kHz

Recent laboratory and epidemiological results have stimulated interest in the hypothesis that human beings may exhibit biological responses to magnetic and/or electric field transients with frequencies in the range between 100 Hz and 100 kHz. Much can be learned about the response of a system to a transient stimulation by understanding its response to sinusoidal disturbances over the entire frequency range of interest. Thus, the main effort of this paper was to compare the strengths of the electric fields induced in homogeneous ellipsoidal models by uniform 100 Hz through 100 kHz electric and magnetic fields. Over this frequency range, external electric fields of about 25–2000 V/m (depending primarily on the orientation of the body relative to the field) are required to induce electric fields inside models of adults and children that are similar in strength to those induced by an external 1 μT magnetic field. Additional analysis indicates that electric fields induced by uniform external electric and magnetic fields and by the nonuniform electric and magnetic fields produced by idealized point sources will not differ by more than a factor of two until the sources are brought close to the body. Published data on electric and magnetic field transients in residential environments indicate that, for most field orientations, the magnetic component will induce stronger electric fields inside adults and children than the electric component. This conclusion is also true for the currents induced in humans by typical levels of 60 Hz electric and magnetic fields in U.S. residences. Bioelectromagnetics 18:67–76, 1997. © 1997 Wiley-Liss, Inc.     

Extremely low frequency electric fields and cancer: Assessing the evidence

Much of the research and reviews on extremely low frequency (ELF) electric and magnetic fields (EMFs) have focused on magnetic rather than electric fields. Some have considered such focus to be inappropriate and have argued that electric fields should be part of both epidemiologic and laboratory work. This paper fills the gap by systematically and critically reviewing electric‐fields literature and by comparing overall strength of evidence for electric versus magnetic fields. The review of possible mechanisms does not provide any specific basis for focusing on electric fields. While laboratory studies of electric fields are few, they do not indicate that electric fields should be the exposure of interest. The existing epidemiology on residential electric‐field exposures and appliance use does not support the conclusion of adverse health effects from electric‐field exposure. Workers in close proximity to high‐voltage transmission lines or substation equipment can be exposed to high electric fields. While there are sporadic reports of increase in cancer in some occupational studies, these are inconsistent and fraught with methodologic problems. Overall, there seems little basis to suppose there might be a risk for electric fields, and, in contrast to magnetic fields, and with a possible exception of occupational epidemiology, there seems little basis for continued research into electric fields. Bioelectromagnetics 31:89–101, 2010. © 2009 Wiley‐Liss, Inc.     

Magnetic alignment in mammals and other animals

Magnetic alignment (MA) constitutes the simplest directional response to the geomagnetic field. In contrast to magnetic compass orientation, MA is not goal directed and represents a spontaneous, fixed directional response. Because animals tend to align their bodies along or perpendicular to the magnetic field lines, MA typically leads to bimodal or quadrimodal orientation, although there is also growing evidence for a fixed unimodal orientation not necessarily coinciding with the magnetic cardinal directions. MA has been demonstrated in diverse animals including insects, amphibians, fish, and mammals. Alignment can be expressed by animals during resting as well as on the move (e.g. while grazing, hunting, feeding, etc.). Here, we briefly survey characteristic features and classical examples of MA and review the current knowledge about the occurrence of MA in mammals. In addition, we summarize what is known about mechanisms underlying MA and discuss its prospective biological functions. Finally, we highlight some physiological effects of alignment along the magnetic field axes reported in humans. We argue that the phenomenon of MA adds a new paradigm that can be exploited for investigation of magnetoreception in mammals.     

Simultaneous analysis of the cardiac electric and magnetic fields using the scalar multipole expansion

A theoretical analysis of electric and magnetic fields of the heart, based solely upon the scalar multipole expansion, is carried out in order to gain an insight into the interrelation of the data contained in electro- and magnetocardiological measurements. The usual multipole expansion is applied for the electric field, however corresp[nding equivalent multipoles are formulated as idealized generators, having not only flow sources, but also vortex sources of the field. Furthermore, the magnetic field in a homogeneous infinite volume conductor is expressed as a sum of two series, the first being the usual multipole expansion of the nonvortex component of the magnetic field, and the second being a sequence of magnetic fields set up by the aforementioned electric multipole generators reduced to axial form. The former term is uniquely defined by the electric multipole components, but the latter reflects properties of the cardiogenerator that can be revealed only by means of magnetic measurements. Features of the electric and magnetic multipole components as integral characteristics of the cardiogenerator are discussed and concepts of the magnetic centre and magnetic axis of the cardiogenerator are proposed. The analysis is illustrated by examples of simple generator configurations.     

Nonlinear Right-Hand Polarized Wave in Plasma in the Electron Cyclotron Resonance Region

The propagation of a nonlinear right-hand polarized wave along an external magnetic field in subcritical plasma in the electron cyclotron resonance region is studied using numerical simulations. It is shown that a small-amplitude plasma wave excited in low-density plasma is unstable against modulation instability with a modulation period equal to the wavelength of the excited wave. The modulation amplitude in this case increases with decreasing detuning from the resonance frequency. The simulations have shown that, for large-amplitude waves of the laser frequency range propagating in plasma in a superstrong magnetic field, the maximum amplitude of the excited longitudinal electric field increases with the increasing external magnetic field and can reach 30% of the initial amplitude of the electric field in the laser wave. In this case, the energy of plasma electrons begins to substantially increase already at magnetic fields significantly lower than the resonance value. The laser energy transferred to plasma electrons in a strong external magnetic field is found to increase severalfold compared to that in isotropic plasma. It is shown that this mechanism of laser radiation absorption depends only slightly on the electron temperature.     

Model Studies of the Magnetocardiogram

A general expression is developed for the quasi-static magnetic field outside an inhomogeneous nonmagnetic volume conductor containing internal electromotive forces. Multipole expansions for both the electric and magnetic fields are derived. It is shown that the external magnetic field vanishes under conditions of axial symmetry. The magnetic field for a dipole current source in a sphere is derived, and the effect of an eccentric spherical inhomogeneity is analyzed. Finally the magnetic dipole moment is calculated for a current dipole in a conducting prolate spheroid.