804 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 7, JULY 2003 On the Induced Electric Field Gradients in the Human Body for Magnetic Stimulation by Gradient Coils in MRI Feng Liu, Huawei Zhao, and Stuart Crozier*, Member, IEEE Abstract—Prior theoretical studies indicate that the negative spatial derivative of the electric field induced by magnetic stim- ulation may be one of the main factors contributing to depolar- ization of the nerve fiber. This paper studies this parameter for pe- ripheral nerve stimulation (PNS) induced by time-varying gradient fields during MRI scans. The numerical calculations are based on an efficient, quasi-static, finite-difference scheme and an anatomi- cally realistic human, full-body model. Whole-body cylindrical and planar gradient sets in MRI systems and various input signals have been explored. The spatial distributions of the induced electric field and their gradients are calculated and attempts are made to corre- late these areas with reported experimental stimulation data. The induced electrical field pattern is similar for both the planar coils and cylindrical coils. This study provides some insight into the spa- tial characteristics of the induced field gradients for PNS in MRI, which may be used to further evaluate the sites where magnetic stimulation is likely to occur and to optimize gradient coil design. Index Terms—Finite difference method, gradient field, human body model, induced electric field gradient, MRI, peripheral nerve stimulation. I. INTRODUCTION I N MAGNETIC resonance imaging (MRI), diffusion weighted, echo-planar imaging (EPI) together with other high-speed imaging methods require large, rapidly switched magnetic field gradients. Stimulation of the peripheral nerve system may be triggered due to these time-varying magnetic fields [1]. In nerve stimulation research, theoretical studies and experiments show that the peripheral nerve may be activated by the first derivative of the component of an induced electric field along a long, straight nerve fiber, during magnetic stimulation [2]–[4]. The positions with large values often correlate with stimulation points. Therefore, the calculation and evaluation of the induced electric field gradients (EFGs) is important to elucidate the underlying mechanisms of the PNS problem Manuscript received April 24, 2002; revised November 11, 2002. This work was supported by the Australian Research Council. Asterisk indicates corre- sponding author. F. Liu is with The School of Information Technology and Electrical Engi- neering, The University of Queensland, St. Lucia, Brisbane, Queensland 4072, Australia. H. Zhao is with The Centre for Magnetic Resonance, The University of Queensland, St. Lucia, Brisbane, Queensland 4072, Australia. *S. Crozier is with The School of Information Technology and Electrical En- gineering, The University of Queensland, St. Lucia, Brisbane, Queensland 4072, Australia (e-mail: Stuart@itee.uq.edu.au). Digital Object Identifier 10.1109/TBME.2003.813538 in modern MRI. This paper provides a numerical solution for the calculation of the EFGs for magnetic stimulation by time-varying gradient fields. We restrict ourselves to the diag- onal elements of the electric field gradient tensor in principal Cartesian coordinates in these studies, while demonstrating our computation method. This is a starting point for the investiga- tions. Full tensor analyzes coupled to nerve orientation models are planned for future work. Many biomedical engineering researchers have been devoted to modeling electromagnetic problems associated with mag- netic stimulation. Several methods, including finite-difference time/frequency-domain, finite element or moment methods have been developed to calculate the fields induced in anatomic models of the human body [5]. Although the finite-element method (FEM) is adaptable to irregular objects and together with the FDTD method provides the full-wave solutions, they usually require long computation time, especially when studying millimeter-resolution human models. In this work, we have used an efficient quasi-static finite difference formulation, based on a realistic model of an adult male with segmented tissue types to calculate the EFGs for nerve stimulation, for both cylindrical and planar gradient coil sets. The method is verified against analytic solutions for low-frequency problems. This effective and simple numerical method allows rapid calculation of EFGs and could, therefore, be combined with a gradient design scheme to generate novel gradient coil configurations with minimal PNS induction. Until recently, only parts of the human/animal body [6]–[9] or simple coil structures [10], [11] were modeled for PNS prob- lems in MRI. Here, we attempt to investigate a more realistic case, i.e., a human body model within a realistic cylindrical gra- dient coil configuration (both longitudinal and transverse coils in conventional MRI) and biplanar Y-coils. Furthermore, we present new calculations for PNS in a variety of MRI environ- ments. II. METHODS A. Numerical Method At low source frequencies, where the dimensions of a bio- logical body are small compared to the wavelength, the induced fields may be able to be treated as quasi-static fields [12]. Ac- cording to Faraday’s law as it relates to a coil structure, the elec- tric field in a sample is generated by time-varying magnetic 0018-9294/03$17.00 © 2003 IEEE