Inr I Rodr ar r on Oncolo~ , Bd Ph,‘J, Vol IO. PP. 1095-l 107 0360.30 I b/X4 $03.00 + .W Pnnt d I” the U.S.A All nghts reserved Copynghl G 1984 Pcrgamon Press Ltd ?? Original Contribution THEORETICAL TEMPERATURE PROFILES FOR CONCENTRIC COIL INDUCTION HEATING DEVICES IN A TWO-DIMENSIONAL, AXI-ASYMMETRIC, INHOMOGENEOUS PATIENT MODEL KEITH D. PAULSEN,’ B.S.E., JOHN W. STROHBEHN, * PH.D., STEVEN C. HILL,* M.S., DANIEL R. LYNCH,’ PH.D. AND FRANCIS E. KENNEDY,’ PH.D. ‘Thayer School of Engineering, Dartmouth College, Hanover, NH 03755; ‘Department of Electrical Engineering, University of Utah, Salt Lake City, UT 84112 In this paper we report on theoretical calculations for the temperature distributions produced by an rf magnetic induction device that is placed concentrically about the long axis of the patient. A two-dimensional, axi-asymmetric, inhomogeneous patient model was used in conjunction with a numerical moment method for calculating the electric fields in the tissues of the model and a numerical finite element method for calculating the resulting temperature distributions. The electric fields and the absorbed power per unit volume of tissue were calculated for both a thorax and viscera model, each of which included a tumor volume. The absorbed power values were input into the bioheat transfer equation aud the temperature distributions were calculated for a wide rauge of blood flow rates. Based on the steady-state and transient results, our computer simuiatious predict poor therapeutic temperature profiles for tumors embedded deeply in the thorax aud viscera. This heating technique appears to produce significant therapeutic volumes in superfkial tumors located not greater than 7 cm in depth. These theoretical calculations should aid the clinician in the evahmtion of induction heating devices for their effectiveness in heating deep-seated and superficial tumors. Hyperthermia, Temperature distributions, Magnetic induction, rf heating, Finite elements. INTRODUCTION Recently, there has been a renewed interest in the use of hyperthermia as a modality for cancer therapy. The toxic effect of temperatures in the range of 42-45’C on both normal and malignant cells is well accepted. Con- siderable effort has been devoted to the design and de- velopment of devices that are capable of producing this range of temperatures within a tumor while minimizing the temperature rise in normal tissue. Despite the variety of systems proposed, built and tested, none of them yet satisfies all of the requirements necessary for wide use in the clinic. Specifically, most systems cannot heat deep seated tumors to therapeutic temperatures. One system designed to address this difficulty is a con- centric coil type inductive device proposed by Storm et &25-27 which is sold under the commercial name “ Mag- netrode” (Henry Medical Electronics, Inc., Los Angeles, CA). With this device, tissue is heated by the power de- posited from eddy currents induced by high frequency magnetic fields generated inside the patient by a cylindrical conducting coil which wraps around the body section to be heated. The Magnetrode has received particular at- tention because it is a commercially available device that is capable of non-invasively depositing significant amounts of power in tissue. As a result of this interest, several investigators have analyzed concentric coil heating systems in order to better understand their advantages and limitations.‘2~‘6~‘7~28 Strohbehn** has calculated the temperature distributions for such devices using the bioheat equation. He assumed a one-dimensional, axi-symmetric patient model which incorporated simple radial variations in tissue parameters such as blood flow. Strohbehn concluded that in most cases a concentric coil type hyperthermia device will not produce a therapeutic temperature rise in tumors deep seated in the abdomen or thorax, but should raise tem- peratures to therapeutic levels in tumors located no deeper than 6 cm within these regions. Halac et al. I2 have made similar calculations, but have included a more complex tumor model and a wider variety of conditions. Steady- state temperature profiles were obtained for the abdominal Supported in part by grants ECS-8025818 from the National Science Foundation and CA 23594 from the National Cancer Institute, DHHS, NIH. Presented at the North American Hyperthetmia Group Meeting, San Antonio, TX, February 27, 1983. Reprint requests to: John W. Strohbehn. Acknowledgements-The authors would like to acknowledge Dr. Carl H. Dumey and Dr. Dot&s A. Christensen for their assistance with the solution of the EM fields. Accepted for publication 2 1 March 1984.