An Improved Quasi-Static Finite-Difference Scheme for Induced Field Evaluation Based on the Biconjugate Gradient Method

This paper presents a biconjugate gradient (BiCG) method that can significantly improve the performance of the quasi-static finite-difference scheme, which has been widely used to model field induction phenomena in voxel phantoms. The proposed BiCG method offers remarkable computational advantages in terms of convergence performance and memory consumption over the conventional iterative, successive overrelaxation algorithm. The scheme has been validated against other known solutions on a lossy, multilayered ellipsoid phantom excited by an ideal coil loop. The wide application capability and computational performance of the BiCG method is demonstrated by modeling the exposure of MRI healthcare workers to fields produced by pulsed field gradients. This is an important topic of research in light of the Physical Agents Directive 2004/40/EC because a variety of realistic operator postures near the bore entrance of an MRI system are modeled.

[1]  P. Dimbylow.  Development of the female voxel phantom, NAOMI, and its application to calculations of induced current densities and electric fields from applied low frequency magnetic and electric fields , 2005, Physics in medicine and biology.

[2]  Hiroshi Kanai,et al.  Impedence Method for Calculation of Power Deposition Patterns in Magnetically Induced Hyperthermia , 1984, IEEE Transactions on Biomedical Engineering.

[3]  C Gabriel,et al.  The dielectric properties of biological tissues: I. Literature survey. , 1996, Physics in medicine and biology.

[4]  F Schmitt,et al.  Physiological effects of fast oscillating magnetic field gradients. , 1991, Journal of computer assisted tomography.

[5]  Gilbert Decat,et al.  Magnetic Fields of Induction Heaters in the Framework of Directive 2004/40/EC of the European Parliament and of the Council , 2006, International journal of occupational safety and ergonomics : JOSE.

[6]  D. Sorensen.  Numerical methods for large eigenvalue problems , 2002, Acta Numerica.

[7]  R M Weisskoff,et al.  Sensory stimulation by time‐varying magnetic fields , 1990, Magnetic resonance in medicine.

[8]  A. Ahlbom.  Guidelines for limiting exposure to time-varying electric, magnetic, and electromagnetic fields (up to 300 GHz) , 1998 .

[9]  S Crozier,et al.  Longitudinal gradient coil optimization in the presence of transient eddy currents , 2007, Magnetic resonance in medicine.

[10]  国際非電離放射線防護委員会.  ICNIRP statement on the "Guidelines for limiting exposure to time-varying electric, magnetic, and electromagnetic fields (up to 300 GHz)". , 2009, Health physics.

[11]  Stuart Crozier,et al.  Finite-difference time-domain-based studies of MRI pulsed field gradient-induced eddy currents inside the human body , 2002 .

[12]  H. Ling,et al.  An efficient wavelet preconditioner for iterative solution of three-dimensional electromagnetic integral equations , 2003 .

[13]  P. Dimbylow.  Current densities in a 2 mm resolution anatomically realistic model of the body induced by low frequency electric fields. , 2000, Physics in medicine and biology.

[14]  Adnan Trakic,et al.  Numerical study of currents in workers induced by body‐motion around high‐ultrahigh field MRI magnets , 2007, Journal of magnetic resonance imaging : JMRI.

[15]  Judith A. Vogel,et al.  Flexible BiCG and flexible Bi-CGSTAB for nonsymmetric linear systems , 2007, Appl. Math. Comput..

[16]  J. Shewchuk.  An Introduction to the Conjugate Gradient Method Without the Agonizing Pain , 1994 .

[17]  F. Liu,et al.  Electromagnetic fields inside a lossy, multilayered spherical head phantom excited by MRI coils: models and methods. , 2004, Physics in medicine and biology.

[18]  Stuart Crozier,et al.  Transient temperature rise in a mouse due to low-frequency regional hyperthermia , 2006, Physics in medicine and biology.

[19]  Seyedeh Mahboubeh Molavi-Arabshahi,et al.  Preconditioned techniques for solving large sparse linear systems arising from the discretization of the elliptic partial differential equations , 2007, Appl. Math. Comput..

[20]  H. V. D. Vorst,et al.  An overview of approaches for the stable computation of hybrid BiCG methods , 1995 .

[21]  Feng Liu,et al.  On the induced electric field gradients in the human body for magnetic stimulation by gradient coils in MRI , 2003, IEEE Transactions on Biomedical Engineering.

[22]  Stuart Crozier,et al.  Numerical study of currents in occupational workers induced by body-motion around high-ultrahigh field MRI magnets , 2007 .

[23]  R. Pethig,et al.  Dielectric properties of body tissues. , 1987, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.

[24]  S. Crozier,et al.  Numerical field evaluation of healthcare workers when bending towards high‐field MRI magnets , 2008, Magnetic resonance in medicine.

[25]  Stuart Crozier,et al.  The Design of Transverse Gradient Coils of Restricted Length by Simulated Annealing , 1994 .

[26]  I. Duff.  A survey of sparse matrix research , 1977, Proceedings of the IEEE.

[27]  F. X. Canning.  Preconditioned iterative solution of IML/moment method problems , 1993 .

[28]  Stuart Crozier,et al.  Exposure of workers to pulsed gradients in MRI , 2007, Journal of magnetic resonance imaging : JMRI.

[29]  Stuart Crozier,et al.  Numerical evaluation of the fields induced by body motion in or near high-field MRI scanners. , 2005, Progress in biophysics and molecular biology.