Finite difference time domain (FDTD) method for modeling the effect of switched gradients on the human body in MRI

Numerical modeling of the eddy currents induced in the human body by the pulsed field gradients in MRI presents a difficult computational problem. It requires an efficient and accurate computational method for high spatial resolution analyses with a relatively low input frequency. In this article, a new technique is described which allows the finite difference time domain (FDTD) method to be efficiently applied over a very large frequency range, including low frequencies. This is not the case in conventional FDTD-based methods. A method of implementing streamline gradients in FDTD is presented, as well as comparative analyses which show that the correct source injection in the FDTD simulation plays a crucial rule in obtaining accurate solutions. In particular, making use of the derivative of the input source waveform is shown to provide distinct benefits in accuracy over direct source injection. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and the source injection method has been verified against examples with analytical solutions. Results are presented showing the spatial distribution of gradient-induced electric fields and eddy currents in a complete body model.

An object-oriented designed finite-difference time-domain simulator for electromagnetic analysis and design in MRI - application to high field analyses

This paper presents a finite-difference time-domain (FDTD) simulator for electromagnetic analysis and design applications in MRI. It is intended to be a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The pro-ram has been constructed in an object-oriented framework. The design procedure is detailed and the numerical solver has been verified against analytical solutions for simple cases and also applied to various field calculation problems. In particular, the simulator is demonstrated for inverse RF coil design, optimized source profile generation, and parallel imaging in high-frequency situations. The examples show new developments enabled by the simulator and demonstrate that the proposed FDTD framework can be used to analyze large-scale computational electromagnetic problems in modern MRI engineering. (C) 2004 Elsevier Inc. All rights reserved.

Finite-difference time-domain-based studies of MRI pulsed field gradient-induced eddy currents inside the human body

In modern magnetic resonance imaging (MRI), patients are exposed to strong, rapidly switching magnetic gradient fields that, in extreme cases, may be able to elicit nerve stimulation. This paper presents theoretical investigations into the spatial distribution of induced current inside human tissues caused by pulsed z-gradient fields. A variety of gradient waveforms have been studied. The simulations are based on a new, high-definition, finite-difference time-domain method and a realistic inhomogeneous 10-mm resolution human body model with appropriate tissue parameters. it was found that the eddy current densities are affected not only by the pulse sequences but by many parameters such as the position of the body inside the gradient set, the local biological material properties and the geometry of the body. The discussion contains a comparison of these results with previous results found in the literature. This study and the new methods presented herein will help to further investigate the biological effects caused by the switched gradient fields in a MRI scan. (C) 2002 Wiley Periodicals, Inc.

A high definition, finite difference time domain method

A high definition, finite difference time domain (HD-FDTD) method is presented in this paper. This new method allows the FDTD method to be efficiently applied over a very large frequency range including low frequencies, which are problematic for conventional FDTD methods. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and has been verified against analytical solutions within the frequency range 50 Hz-1 GHz. As an example of the lower frequency range, the method has been applied to the problem of induced eddy currents in the human body resulting from the pulsed magnetic field gradients of an MRI system. The new method only requires approximately 0.3% of the source period to obtain an accurate solution. (C) 2003 Elsevier Science Inc. All rights reserved.

An FDTD model for calculation of gradient-induced eddy currents in MRI system

In most magnetic resonance imaging (MRI) systems, pulsed magnetic gradient fields induce eddy currents in the conducting structures of the superconducting magnet. The eddy currents induced in structures within the cryostat are particularly problematic as they are characterized by long time constants by virtue of the low resistivity of the conductors. This paper presents a three-dimensional (3-D) finite-difference time-domain (FDTD) scheme in cylindrical coordinates for eddy-current calculation in conductors. This model is intended to be part of a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The singularity apparent in the governing equations is removed by using a series expansion method and the conductor-air boundary condition is handled using a variant of the surface impedance concept. The numerical difficulty due to the asymmetry of Maxwell equations for low-frequency eddy-current problems is circumvented by taking advantage of the known penetration behavior of the eddy-current fields. A perfectly matched layer absorbing boundary condition in 3-D cylindrical coordinates is also incorporated. The numerical method has been verified against analytical solutions for simple cases. Finally, the algorithm is illustrated by modeling a pulsed field gradient coil system within an MRI magnet system. The results demonstrate that the proposed FDTD scheme can be used to calculate large-scale eddy-current problems in materials with high conductivity at low frequencies.

Numerical modeling of 11.1 T MRI of a human head using MoM/FDTD methods

In a recent study, severe distortions in the proton images of an excised, fixed, human brain in an 11.1 Tesla/40 cm MR instrument have been observed, and the effect modeled on phantom images using a finite difference time domain (FDTD) model. in the present study, we extend these simulations to that of a complete human head, employing a hybrid FDTD and method of moments (MoM) approach, which provides a validated method for simulating biological samples in coil structures. The effect of fixative on the image distortions is explored. importantly, temperature distributions within the head are also simulated using a bioheat method based on parameters derived from the electromagnetic simulations. The MoM/FDTD simulations confirm that the transverse magnetic field (B,) from a ReCav resonator exhibits good homogeneity in air but strong inhomogeneity when loaded with the head with or without fixative. The fixative serves to increase the distortions, but they are still significant for the in vivo simulations. The simulated signal intensity (SI) distribution within the sample confirm the distortions in the experimental images are caused by the complex interactions of the incident electromagnetic fields with tissue, which is heterogeneous in terms of conductivity and permittivity. The temperature distribution is likewise heterogeneous, raising concerns regarding hot spot generation in the sample that may exceed acceptable levels in future in vivo studies. As human imaging at 11.1 T is some time away, simulations are important in terms of predicting potential safety issues as well as evaluating practical concerns about the quality of images. Simulation on a whole human head at 11.1 T implies the wave behavior presents significant engineering challenges for ultra-high-field (UHF) MRI. Novel strategies will have to be employed in imaging technique and resonator design for UHF MRI to achieve the theoretical signal-to-noise ratio (SNR) improvements it offers over lower field systems. (C) 2005 Wiley Periodicals, Inc.

Analysis of transient eddy currents in MRI using a cylindrical FDTD method

Most magnetic resonance imaging (MRI) spatial encoding techniques employ low-frequency pulsed magnetic field gradients that undesirably induce multiexponentially decaying eddy currents in nearby conducting structures of the MRI system. The eddy currents degrade the switching performance of the gradient system, distort the MRI image, and introduce thermal loads in the cryostat vessel and superconducting MRI components. Heating of superconducting magnets due to induced eddy currents is particularly problematic as it offsets the superconducting operating point, which can cause a system quench. A numerical characterization of transient eddy current effects is vital for their compensation/control and further advancement of the MRI technology as a whole. However, transient eddy current calculations are particularly computationally intensive. In large-scale problems, such as gradient switching in MRI, conventional finite-element method (FEM)-based routines impose very large computational loads during generation/solving of the system equations. Therefore, other computational alternatives need to be explored. This paper outlines a three-dimensional finite-difference time-domain (FDTD) method in cylindrical coordinates for the modeling of low-frequency transient eddy currents in MRI, as an extension to the recently proposed time-harmonic scheme. The weakly coupled Maxwell's equations are adapted to the low-frequency regime by downscaling the speed of light constant, which permits the use of larger FDTD time steps while maintaining the validity of the Courant-Friedrich-Levy stability condition. The principal hypothesis of this work is that the modified FDTD routine can be employed to analyze pulsed-gradient-induced, transient eddy currents in superconducting MRI system models. The hypothesis is supported through a verification of the numerical scheme on a canonical problem and by analyzing undesired temporal eddy current effects such as the B-0-shift caused by actively shielded symmetric/asymmetric transverse x-gradient head and unshielded z-gradient whole-body coils operating in proximity to a superconducting MRI magnet.

High-field magnetic resonance imaging with reduced field/tissue RF artefacts - A modeling study using hybrid MoM/FEM and FDTD technique

Due to complex field/tissue interactions, high-field magnetic resonance (MR) images suffer significant image distortions that result in compromised diagnostic quality. A new method that attempts to remove these distortions is proposed in this paper and is based on the use of transceiver-phased arrays. The proposed system uses, in the examples presented herein, a shielded four-element transceive-phased array head coil and involves performing two separate scans of the same slice with each scan using different excitations during transmission. By optimizing the amplitudes and phases for each scan, antipodal signal profiles can be obtained, and by combining both the images together, the image distortion can be reduced several fold. A combined hybrid method of moments (MoM)/finite element method (FEM) and finite-difference time-domain (FDTD) technique is proposed and used to elucidate the concept of the new method and to accurately evaluate the electromagnetic field (EMF) in a human head model. In addition, the proposed method is used in conjunction with the generalized auto-calibrating partially parallel acquisitions (GRAPPA) reconstruction technique to enable rapid imaging of the two scans. Simulation results reported herein for 11-T (470-MHz) brain imaging applications show that the new method with GRAPPA reconstruction theoretically results in improved image quality and that the proposed combined hybrid MoM/FEM and FDTD technique is. suitable for high-field magnetic resonance imaging (MRI) numerical analysis.

An object-orient designed FDTD simulator: Applications to high field systems

An object-oriented finite-difference time-domain (FDTD) simulator has been developed for electromagnetic study and design applications in Magnetic Resonance Imaging. It is aimed to be a complete FDTD model of an MRI system including all high and low-frequency field generating units and electrical models of the patient. The design method is described and MRI-based numerical examples are presented to illustrate the function of the numerical solver, particular emphasis is placed on high field studies.

FDTD study of an UWB radar technique for breast tumor detection

A finite difference time domain (FDTD) method is applied to investigate capabilities of an ultra-wide band (UWB) radar system to detect a breast tumor. The first part of the investigations concerns FDTD simulations of a phantom formed by a plastic container with liquid and a small reflecting target. The second part focuses on a three-dimensional numerical breast model with a small tumor. FDTD simulations are carried out assuming a planar incident wave. Various time snap shots of the electromagnetic field are recorded to learn about the physical phenomenon of reflection and scattering in different layers of the phantom.

Numerical modelling of thermal effects in rats due to high-field magnetic resonance imaging (0.5-1 GHz)

A finite-difference time-domain (FDTD) thermal model has been developed to compute the temperature elevation in the Sprague Dawley rat due to electromagnetic energy deposition in high-field magnetic resonance imaging (MRI). The field strengths examined ranged from 11.75-23.5 T (corresponding to H-1 resonances of 0.5-1 GHz) and an N-stub birdcage resonator was used to both transmit radio-frequency energy and receive the MRI signals. With an in-plane resolution of 1.95 mm, the inhomogeneous rat phantom forms a segmented model of 12 different tissue types, each having its electrical and thermal parameters assigned. The steady-state temperature distribution was calculated using a Pennes 'bioheat' approach. The numerical algorithm used to calculate the induced temperature distribution has been successfully validated against analytical solutions in the form of simplified spherical models with electrical and thermal properties of rat muscle. As well as assisting with the design of MRI experiments and apparatus, the numerical procedures developed in this study could help in future research and design of tumour-treating hyperthermia applicators to be used on rats in vivo.

Computational modeling of optical trapping of vaterite microspheres

The ability to grow microscopic spherical birefringent crystals of vaterite, a calcium carbonate mineral, has allowed the development of an optical microrheometer based on optical tweezers. However, since these crystals are birefringent, and worse, are expected to have non-uniform birefringence, computational modeling of the microrheometer is a highly challenging task. Modeling the microrheometer - and optical tweezers in general - typically requires large numbers of repeated calculations for the same trapped particle. This places strong demands on the efficiency of computational methods used. While our usual method of choice for computational modelling of optical tweezers - the T-matrix method - meets this requirement of efficiency, it is restricted to homogeneous isotropic particles. General methods that can model complex structures such as the vaterite particles, such as finite-difference time-domain (FDTD) or finite-difference frequency-domain (FDFD) methods, are inefficient. Therefore, we have developed a hybrid FDFD/T-matrix method that combines the generality of volume-discretisation methods such as FDFD with the efficiency of the T-matrix method. We have used this hybrid method to calculate optical forces and torques on model vaterite spheres in optical traps. We present and compare the results of computational modelling and experimental measurements.

Tailoring magnetic field gradient design to magnet cryostat geometry

Eddy currents induced within a magnetic resonance imaging (MRI) cryostat bore during pulsing of gradient coils can be applied constructively together with the gradient currents that generate them, to obtain good quality gradient uniformities within a specified imaging volume over time. This can be achieved by simultaneously optimizing the spatial distribution and temporal pre-emphasis of the gradient coil current, to account for the spatial and temporal variation of the secondary magnetic fields due to the induced eddy currents. This method allows the tailored design of gradient coil/magnet configurations and consequent engineering trade-offs. To compute the transient eddy currents within a realistic cryostat vessel, a low-frequency finite-difference time-domain (FDTD) method using total-field scattered-field (TFSF) scheme has been performed and validated

A distributed equivalent magnetic current based FDTD method for the calculation of E-fields induced by gradient coils

This paper evaluates a new, low-frequency finite-difference time-domain method applied to the problem of induced E-fields/eddy currents in the human body resulting from the pulsed magnetic field gradients in MRI. In this algorithm, a distributed equivalent magnetic current is proposed as the electromagnetic source and is obtained by quasistatic calculation of the empty coil's vector potential or measurements therein. This technique circumvents the discretization of complicated gradient coil geometries into a mesh of Yee cells, and thereby enables any type of gradient coil modelling or other complex low frequency sources. The proposed method has been verified against an example with an analytical solution. Results are presented showing the spatial distribution of gradient-induced electric fields in a multi-layered spherical phantom model and a complete body model. (C) 2004 Elsevier Inc. All rights reserved.