Investigation on magnetoacoustic signal generation with magnetic induction and its application to electrical conductivity reconstruction

A theoretical study on the magnetoacoustic signal generation with magnetic induction and its applications to electrical conductivity reconstruction is conducted. An object with a concentric cylindrical geometry is located in a static magnetic field and a pulsed magnetic field. Driven by Lorentz force generated by the static magnetic field, the magnetically induced eddy current produces acoustic vibration and the propagated sound wave is received by a transducer around the object to reconstruct the corresponding electrical conductivity distribution of the object. A theory on the magnetoacoustic waveform generation for a circular symmetric model is provided as a forward problem. The explicit formulae and quantitative algorithm for the electrical conductivity reconstruction are then presented as an inverse problem. Computer simulations were conducted to test the proposed theory and assess the performance of the inverse algorithms for a multi-layer cylindrical model. The present simulation results confirm the validity of the proposed theory and suggest the feasibility of reconstructing electrical conductivity distribution based on the proposed theory on the magnetoacoustic signal generation with magnetic induction.     

Magnetic field effects on the vestibular system: calculation of the pressure on the cupula due to ionic current-induced Lorentz force

Large static magnetic fields may be employed in magnetic resonance imaging (MRI). At high magnetic field strengths (usually from about 3 T and above) it is possible for humans to perceive a number of effects. One such effect is mild vertigo. Recently, Roberts et al (2011 Current Biology 21 1635-40) proposed a Lorentz-force mechanism resulting from the ionic currents occurring naturally in the endolymph of the vestibular system. In the present work a more detailed calculation of the forces and resulting pressures in the vestibular system is carried out using a numerical model. Firstly, realistic 3D finite element conductivity and fluid maps of the utricle and a single semi-circular canal containing the current sources (dark cells) and sinks (hair cells) of the utricle and ampulla were constructed. Secondly, the electrical current densities in the fluid are calculated. Thirdly, the developed Lorentz force is used directly in the Navier-Stokes equation and the trans-cupular pressure is computed. Since the driving force field is relatively large in comparison with the advective acceleration, we demonstrate that it is possible to perform an approximation in the Navier-Stokes equations that reduces the problem to solving a simpler Poisson equation. This simplification allows rapid and easy calculation for many different directions of applied magnetic field. At 7 T a maximum cupula pressure difference of 1.6 mPa was calculated for the combined ampullar (0.7?μA) and utricular (3.31?μA) distributed current sources, assuming a hair-cell resting current of 100 pA per unit. These pressure values are up to an order of magnitude lower than those proposed by Roberts et al using a simplistic model and calculation, and are in good agreement with the estimated pressure values for nystagmus velocities in caloric experiments. This modeling work supports the hypothesis that the Lorentz force mechanism is a significant contributor to the perception of magnetic field induced vertigo.     

3-D simulation of light scattering from biological cells and cell differentiation

A 3-D code for solving the set of Maxwell equations with the finite-difference time-domain method is developed for simulating the propagation and scattering of light in biological cells under realistic conditions. The numerical techniques employed in this code include the Yee algorithm, absorbing boundary conditions, the total field/scattered field formulation, the discrete Fourier transformation, and the near-to-far field transform using the equivalent electric and magnetic currents. The code is capable of simulating light scattering from any real cells with complex internal structure at all angles, including backward scattering. The features of the scattered light patterns in different situations are studied in detail with the objective of optimizing the performance of cell diagnostics employing cytometry. A strategy for determining the optimal angle for measuring side scattered light is suggested. It is shown that cells with slight differences in their intrastructure can be distinguished with two-parameter cytometry by measuring the side scattered light at optimal angles.     

Electric current generated by ultrasonically induced Lorentz force in biological media

The ions of solutions exposed to the propagation of ultrasound in the presence of a magnetic field experience Lorentz force. Their movement gives rise to a local electric current density, which is proportional to the electric conductivity of the medium. In vitro assessment of this current is performed using simple models of biological media. A constant magnetic field of 0.35T and 500kHz pulsed ultrasound are used. The sensing electrodes are exposed to neither the pressure wave nor the magnetic field, thus ensuring that the signal is not due to any undesirable electrode effect. The experimental results confirm that the current is proportional to the electrical conductivity of the medium. The changes in the measured current against the width of the measurement chamber show that the electrodes only collect fraction of the current created within the medium. The magnitude of the measured current is 50nA in a saline solution of 0.5S/m conductivity. The technique enabled the determination of the conductivity of a porcine blood sample against haematocrit. It is concluded that this type of measurement has the potential to allow the electrical conductivity of a medium to be determined using ultrasound.     

磁声成像方法的研究进展

磁声成像技术（MAT）是电阻抗成像与超声成像相结合的一种方法。感应式磁声成像方法是将被测样本置于静磁场和交变磁场中,交变磁场在样本中产生涡流,涡流受到洛仑兹力作用而激发出超声波,通过检测超声信号重建电阻抗的分布。应用感应式磁声成像方法可以获得较高分辨率的图像和灵敏度,对临床辅助诊断具有重要意义。并在此基础上提出了无需旋转静磁场的感应式磁声成像方法。     

The movement of a nerve in a magnetic field: application to MRI Lorentz effect imaging

Direct detection of neural activity with MRI would be a breakthrough innovation in brain imaging. A Lorentz force method has been proposed to image nerve activity using MRI; a force between the action currents and the static MRI magnetic field causes the nerve to move. In the presence of a magnetic field gradient, this will cause the spins to precess at a different frequency, affecting the MRI signal. Previous mathematical modeling suggests that this effect is too small to explain the experimental data, but that model was limited because the action currents were assumed to be independent of position along the nerve and because the magnetic field was assumed to be perpendicular to the nerve. In this paper, we calculate the nerve displacement analytically without these two assumptions. Using realistic parameter values, the nerve motion is <5 nm, which induced a phase shift in the MRI signal of <0.02°. Therefore, our results suggest that Lorentz force imaging is beyond the capabilities of current technology.     

Experimental verification of magnetic field dose effects for the MRI-accelerator

The MRI-linear accelerator system, currently being developed, is designed such that the patient is irradiated in the presence of a magnetic field. This influences the dose distribution due to the Lorentz force working on the secondary electrons. Simulations have shown that the following dose effects occur: the build-up distance is reduced, the lateral profile becomes asymmetric in the direction orthogonal to the magnetic field and at tissue-air interfaces the dose increases due to returning electrons. In this work, GafChromic film measurements were performed in the presence of a magnetic field to experimentally quantify these dose effects. Depth-dose curves were measured in a PMMA-air-PMMA phantom and the lateral profiles were measured in a homogeneous PMMA phantom with the photon beam protruding over the edges of the phantom. The measurement results confirmed the magnetic field dose effects that were predicted by simulations. This enabled us to verify Geant4 Monte Carlo simulations of these MRI-linac specific dose effects: the relative agreement for the depth-dose curves between measurements and simulations was within 2.2%/1.8 mm. The relative agreement for the lateral profiles was 2.3%/1.7 mm. Overall, the magnetic field dose effects that are expected for irradiation with the MRI-linac can be modelled using Geant4 Monte Carlo simulations within measurement accuracy.     

Designing a Hemispherical Breast RF Coil Array for MRI

In this paper, an approach to the design of hemispherical breast RF coil array is proposed. The target field method is applied to find the current density distribution on the hemisphere surface, which induces a homogeneous magnetic field in a hemispherical volume. The components of current density are expanded into Fourier series, and the highly ill-conditioned character of the linear equation related to Fourier coefficients is solved using the Tikhonov regularization method with a minimum curvature penalty function. The winding pattern was acquired using the stream function technique. The results indicate that a simple winding pattern with homogeneous magnetic field can be obtained through manually selecting the penalty factor.     

A new method for spatially selective,non-invasive activation of neurons: concept and computer simulation

Currently available non-invasive neurostimulation devices, using skin electrodes or externally applied magnetic coils, are not capable of producing a local stimulation maximum deep inside a homogeneous conductor, because of a fundamental limitation inherent to the Laplace equation. In this paper, a new neurostimulation method (the DeepFocus method) is presented, which avoids this limitation by using an indirect method of producing electric currents inside tissues: First, cylinder-shaped ferromagnetic rotating disks of non-permanent magnetic material are placed near the skin and magnetized by a non-rotating magnetic coil. Each of the disks rotates at high speed around its own axis of symmetry, thus producing a purely electric Lorentz force field having a non-zero divergence outside the disk, and therefore giving rise to charge accumulations inside the tissues. Subsequently, the magnetic field is switched off suddenly, causing a re-distribution of charge, and hence short-lived electrical currents, which can be used to activate neurons. Two magnet configurations are presented in this paper, and analyzed by computer simulation, showing that the DeepFocus method produces a maximum current density (the ‘focus’) deep inside the conducting body. The field strength thus created in the focus (7.9 V/m) is strong enough to activate thick myelinated fibers, but can be kept below the threshold for C-fibers, which makes the new method a possible tool for pain mitigation by targeted neurostimulation.     

Sensitivity of EEG and MEG measurements to tissue conductivity

Monitoring the electrical activity inside the human brain using electrical and magnetic field measurements requires a mathematical head model. Using this model the potential distribution in the head and magnetic fields outside the head are computed for a given source distribution. This is called the forward problem of the electro-magnetic source imaging. Accurate representation of the source distribution requires a realistic geometry and an accurate conductivity model. Deviation from the actual head is one of the reasons for the localization errors. In this study, the mathematical basis for the sensitivity of voltage and magnetic field measurements to perturbations from the actual conductivity model is investigated. Two mathematical expressions are derived relating the changes in the potentials and magnetic fields to conductivity perturbations. These equations show that measurements change due to secondary sources at the perturbation points. A finite element method (FEM) based formulation is developed for computing the sensitivity of measurements to tissue conductivities efficiently. The sensitivity matrices are calculated for both a concentric spheres model of the head and a realistic head model. The rows of the sensitivity matrix show that the sensitivity of a voltage measurement is greater to conductivity perturbations on the brain tissue in the vicinity of the dipole, the skull and the scalp beneath the electrodes. The sensitivity values for perturbations in the skull and brain conductivity are comparable and they are, in general, greater than the sensitivity for the scalp conductivity. The effects of the perturbations on the skull are more pronounced for shallow dipoles, whereas, for deep dipoles, the measurements are more sensitive to the conductivity of the brain tissue near the dipole. The magnetic measurements are found to be more sensitive to perturbations near the dipole location. The sensitivity to perturbations in the brain tissue is much greater when the primary source is tangential and it decreases as the dipole depth increases. The resultant linear system of equations can be used to update the initially assumed conductivity distribution for the head. They may be further exploited to image the conductivity distribution of the head from EEG and/or MEG measurements. This may be a fast and promising new imaging modality.     

Image reconstruction of anisotropic conductivity tensor distribution in MREIT: computer simulation study

We describe a novel method of reconstructing images of an anisotropic conductivity tensor distribution inside an electrically conducting subject in magnetic resonance electrical impedance tomography (MREIT). MREIT is a recent medical imaging technique combining electrical impedance tomography (EIT) and magnetic resonance imaging (MRI) to produce conductivity images with improved spatial resolution and accuracy. In MREIT, we inject electrical current into the subject through surface electrodes and measure the z-component Bz of the induced magnetic flux density using an MRI scanner. Here, we assume that z is the direction of the main magnetic field of the MRI scanner. Considering the fact that most biological tissues are known to have anisotropic conductivity values, the primary goal of MREIT should be the imaging of an anisotropic conductivity tensor distribution. However, up to now, all MREIT techniques have assumed an isotropic conductivity distribution in the image reconstruction problem to simplify the underlying mathematical theory. In this paper, we firstly formulate a new image reconstruction method of an anisotropic conductivity tensor distribution. We use the relationship between multiple injection currents and the corresponding induced Bz data. Simulation results show that the algorithm can successfully reconstruct images of anisotropic conductivity tensor distributions. While the results show the feasibility of the method, they also suggest a more careful design of data collection methods and data processing techniques compared with isotropic conductivity imaging.     

Integrating a MRI scanner with a 6 MV radiotherapy accelerator: impact of the surface orientation on the entrance and exit dose due to the transverse magnetic field

At the UMC Utrecht, in collaboration with Elekta and Philips Research Hamburg, we are developing a radiotherapy accelerator with integrated MRI functionality. The radiation dose will be delivered in the presence of a lateral 1.5 T field. Although the photon beam is not affected by the magnetic field, the actual dose deposition is done by a cascade of secondary electrons and these electrons are affected by the Lorentz force. The magnetic field causes a reduced build-up distance: because the trajectory of the electrons between collisions is curved, the entrance depth in tissue decreases. Also, at tissue-air interfaces an increased dose occurs due to the so-called electron return effect (ERE): electrons leaving tissue will describe a circular path in air and re-enter the tissue yielding a local dose increase. In this paper the impact of a 1.5 T magnetic field on both the build-up distance and the dose increase due to the ERE will be investigated as a function of the angle between the surface and the incident beam. Monte Carlo simulations demonstrate that in the presence of a 1.5 T magnetic field, the surface dose, the build-up distance and the exit dose depend more heavily on the surface orientation than in the case without magnetic field. This is caused by the asymmetrical pointspread kernel in the presence of 1.5 T and the directional behaviour of the re-entering electrons. Simulations on geometrical phantoms show that ERE dose increase at air cavities can be avoided using opposing beams, also when the air-tissue boundary is not perpendicular to the beam. For the more general case in patient anatomies, more problems may arise. Future work will address the possibilities and limitations of opposing beams in combination with IMRT in a magnetic field.     

Fast dose calculation in magnetic fields with GPUMCD

A new hybrid imaging-treatment modality, the MRI-Linac, involves the irradiation of the patient in the presence of a strong magnetic field. This field acts on the charged particles, responsible for depositing dose, through the Lorentz force. These conditions require a dose calculation engine capable of taking into consideration the effect of the magnetic field on the dose distribution during the planning stage. Also in the case of a change in anatomy at the time of treatment, a fast online replanning tool is desirable. It is improbable that analytical solutions such as pencil beam calculations can be efficiently adapted for dose calculations within a magnetic field. Monte Carlo simulations have therefore been used for the computations but the calculation speed is generally too slow to allow online replanning. In this work, GPUMCD, a fast graphics processing unit (GPU)-based Monte Carlo dose calculation platform, was benchmarked with a new feature that allows dose calculations within a magnetic field. As a proof of concept, this new feature is validated against experimental measurements. GPUMCD was found to accurately reproduce experimental dose distributions according to a 2%-2 mm gamma analysis in two cases with large magnetic field-induced dose effects: a depth-dose phantom with an air cavity and a lateral-dose phantom surrounded by air. Furthermore, execution times of less than 15 s were achieved for one beam in a prostate case phantom for a 2% statistical uncertainty while less than 20 s were required for a seven-beam plan. These results indicate that GPUMCD is an interesting candidate, being fast and accurate, for dose calculations for the hybrid MRI-Linac modality.     

Lattice Boltzmann simulation of thermofluidic transport phenomena in a DC magnetohydrodynamic (MHD) micropump

A comprehensive non-isothermal Lattice Boltzmann (LB) algorithm is proposed in this article to simulate the thermofluidic transport phenomena encountered in a direct-current (DC) magnetohydrodynamic (MHD) micropump. Inside the pump, an electrically conducting fluid is transported through the microchannel by the action of an electromagnetic Lorentz force evolved out as a consequence of the interaction between applied electric and magnetic fields. The fluid flow and thermal characteristics of the MHD micropump depend on several factors such as the channel geometry, electromagnetic field strength and electrical property of the conducting fluid. An involved analysis is carried out following the LB technique to understand the significant influences of the aforementioned controlling parameters on the overall transport phenomena. In the LB framework, the hydrodynamics is simulated by a distribution function, which obeys a single scalar kinetic equation associated with an externally imposed electromagnetic force field. The thermal history is monitored by a separate temperature distribution function through another scalar kinetic equation incorporating the Joule heating effect. Agreement with analytical, experimental and other available numerical results is found to be quantitative.     

An analytical solution to proton Bragg peak deflection in a magnetic field

The role of MR imaging for image-guided radiation therapy (IGRT) is becoming more and more important thanks to the excellent soft tissue contrast offered by MRI. Hybrid therapy devices with integrated MRI scanners are under active development for x-ray therapy. The combination of proton therapy with MRI imaging has only been investigated at the theoretical or conceptual level. Of concern is the deflection of the proton beam in the homogeneous magnetic field. A previous publication has come to the conclusion that the impact of a 0.5 T magnetic field on the dose distribution for proton therapy is very small and lateral deflections stay well below 2?mm. The purpose of this study is to provide new insights into the effects of magnetic fields on a proton beam coming to rest in a patient. We performed an analytical calculation of the lateral deflection of protons with initial energies between 50 MeV and 250 MeV, perpendicular to the beam direction and the magnetic field. We used a power-law range-energy relationship and the Lorentz force in both relativistic and non-relativistic conditions. Calculations were done for protons coming to rest in water or soft tissue, and generalized to other uniform and non-uniform media. Results were verified by comparisons with numerical calculations and Monte Carlo simulations. A key result of our calculations is that the maximum lateral deflection at the end of range is proportional to the third power of the initial energy. Accordingly, due to the strong dependence on the energy, even a relatively small magnetic field of 0.5 T will cause a deflection of the proton beam by 1?cm at the end of range of a 200 MeV beam. The maximum deflection at 200 MeV is more than 10?times larger than that of a 90 MeV beam. Relativistic corrections of the deflection are generally small but they can become non-negligible at higher energies around 200 MeV and above. Contrary to previous findings, the lateral deflection of a proton beam can be significant (1?cm and above) even in relatively small magnetic fields of 0.5 T. However, the curved path of a proton beam in a magnetic field is easily predictable and it should be possible to account for this in treatment planning.     

An electrodeless measuring technique for determining conductivity of biological tissues at radio frequencies

An electrodeless measuring technique for determining the conductivity of biological tissues at radio frequencies is described. The technique is based on measuring magnetic power dissipation in a conducting sample using a tuned circuit when the sample is immersed in a time-varying magnetic field. Theory regarding the measurements is presented. Consideration for coil design is given. Coil construction and measurement techniques are described in detail. The technique has three advantages: errors resulting from electrode lead inductance are completely removed; contacts between tissue surfaces and electrode surfaces are not needed; and maintaining water content and concentration of pH solution inside the tissues during measurements becomes easily facilitated. With the technique, conductivity values of dog kidney at room temperature were obtained in good agreement with previous work.     

A new method for application of force to cells via ferric oxide beads

 We describe a new method that uses straightforward physics to apply force to substrate-attached cells. In this method, collagen-coated magnetic ferric oxide beads attach to the dorsal surface of cells via receptors of the integrin family, and a magnetic field gradient is applied to produce a force. In this paper we present a complete characterization of the method in a configuration that is easy to use, in which a permanent magnet provides a fairly uniform gradient over a relatively large area. This allows a fairly uniform average force that can be controlled in magnitude, direction, and duration to be applied to a large number of cells. We show how to determine the applied force per cell by measuring the force per unit volume of magnetic bead, the distribution of bead diameters, and the distribution of beads per cell. We also show how to calculate the force per unit volume of bead in a three-dimensional region near the permanent magnet on the basis of field measurements, and present results for three of the magnets. An upward force applied to fibroblasts by this method produces a measurable time-dependent increase in attachment of cytoskeletal actin filaments to the force application points, and an increase in actin cross-linking. This is accompanied by an actin-dependent retraction of the force-induced upward movement of the dorsal surface of the cells. Received: 27 February 1997 / Received after revision: 10 August 1997 / Accepted: 1 September 1997     

The potential induced in anisotropic tissue by the ultrasonically-induced Lorentz force

In the presence of a magnetic field, an ultrasonic wave propagating through tissue will induce Lorentz forces on the ions, resulting in an electrical current. If the electrical conductivity is anisotropic, this current is tilted toward the fiber direction, causing charge to accumulate between half-wavelengths: positive charge where the current vectors converge and negative where the current vectors diverge. This charge produces an electric field in the direction of propagation that is associated with an electrical potential, and this electric field causes an additional current that is also tilted by the anisotropy. The final result is the total current pointing perpendicular to the direction of propagation and a charging of the tissue every half wavelength. The potential has a greater magnitude than that obtained from colloidal suspensions or ionic solutions (ultrasonic vibration potentials) and may be used as the basis of a technique to image conductivity.     

A trail of artificial vestibular stimulation: electricity, heat, and magnet

The interaction between the magnetic field of a magnetic resonance imaging (MRI) machine and ion currents within the inner-ear endolymph results in a Lorentz force. This force produces a pressure that pushes on the cupula within the semicircular canals causing nystagmus and vertigo. Here I discuss several implications of this unique and noninvasive way to stimulate the vestibular system in experimental neurophysiology and clinical neurology.     

The fast Padé transform in magnetic resonance spectroscopy for potential improvements in early cancer diagnostics

The convergence rates of the fast Padé transform (FPT) and the fast Fourier transform (FFT) are compared. These two estimators are used to process a time-signal encoded at 4 T by means of one-dimensional magnetic resonance spectroscopy (MRS) for healthy human brain. It is found systematically that at any level of truncation of the full signal length, the clinically relevant resonances that determine concentrations of metabolites in the investigated tissue are significantly better resolved in the FPT than in the FFT. In particular, the FPT has a better resolution than the FFT for the same signal length. Moreover, the FPT can achieve the same resolution as the FFT by using twice shorter signals. Implications of these findings for two-dimensional magnetic resonance spectroscopy as well as for two- and three-dimensional magnetic resonance spectroscopic imaging are highlighted. Self-contained cross-validation of all the results from the FPT is secured by using two conceptually different, equivalent algorithms (inside and outside the unit-circle), that are both valid in the entire complex frequency plane. The difference between the results from these two variants of the FPT is indistinguishable from the background noise. This constitutes robust error analysis of proven validity. The FPT shows promise in applications of MRS for early cancer detection.