Temperature field estimation using electrical impedance profiling methods. I. Reconstruction algorithm and simulated results

Algorithmic methods for estimating complete temperature fields during hyperthermia treatments based on surface and internal electrical measurements are presented. The techniques utilized draw upon impedance imaging concepts, but rather than limit the measurements to positions on the body surface, internal impedance recording sites are allowed. Theoretical simulations show that this strategy improves the reconstructed image in the target region when either internal measurement locations are added to a given number of external recording sites or some external measurement locations are replaced by internal recording positions. The algorithms developed are tested on a set of problems with increasing levels of complexity. The culmination of these investigations is a complete simulation of a hyperthermia treatment and reconstruction of a thermal image for a body cross-section of an actual cancer patient. The results of this work suggest that the surface plus internal measurement approach holds some promise as a method for estimating temperature distributions during hyperthermia treatments. However, the simulations while promising are idealizations in that they are two-dimensional with modest levels of additive noise. In a companion paper, we explore the viability of this approach in several laboratory phantom experiments which include both static and heat-induced transient electrical property profiles.

Temperature field estimation using electrical impedance profiling methods. II. Experimental system description and phantom results

An electrical impedance tomography system has been developed and tested for the purpose of thermal imaging. Since impedance changes with temperature, images of impedance subtracted from normothermic baselines will provide a map of temperature data. A system was designed to be operational at 10-50 kHz and to utilize 16 external electrodes around the periphery of a tissue-equivalent phantom encompassing the region of interest. These electrodes serve as current sources for the 5 mA constant-current inputs and are also used for reading differential voltages. Hyperthermia treatments for cancer require that internal thermometry probes be inserted into the tumour volume. Linear arrays of electrodes with thermometry tracks for micro-dimension thermometry serve this function, as well as providing localized voltage measurements in the region of interest. The embedded temperature sensors provide a quality assurance and calibration standard for the linear arrays in reconstruction of impedance profiles. Results of transient heating experiments with conductive and ultrasound heating are shown where image reconstruction is performed using a finite element model. Temperature predictions in these studies were accurate to better than 1 degree C on average when using information from surface electrodes combined with internal linear arrays. Maximum temperature errors, however, was found to be > 5 degrees C which suggests that further noise reduction during data acquisition and improvements in the reconstructions algorithms are needed.

Finite element computations of specific absorption rates in anatomically conforming full-body models for hyperthermia treatment analysis

Finite element techniques for three-dimensional specific absorption rate (SAR) computation in anatomically based human models are presented. The formulations center on Helmholtz weak forms which have been shown to be numerically robust and to afford additional sparsity in the resulting system of algebraic equations. Practical solution of these equations depends critically on the realization of an effective sparse matrix solver. Experience with several conjugate gradient-type methods is reported. The findings show that convergence rate (and even convergence in some cases) degrades significantly with increasing matrix rank and decreasing electrical loss for mesh spacings which adequately resolve the physical wavelengths of the electromagnetic wave propagation. However, with proper choice of algorithm and preconditioning, reliable convergence has been achieved for matrix ranks exceeding 2 x 10(5) on domains having sizeable volumes of electrically lossless regions. An automatic grid generation scheme for constructing meshes which consist of variable element sizes that conform to a predefined set of boundaries is discussed. Example meshes of homogeneous and heterogeneous human anatomies, the boundaries of which have been derived from CT-scan information, are shown. These results highlight the fact that 3D finite element mesh generation remains a difficult problem, but usable meshes with this level of complexity can be generated. Integration of the finite element formulation, the sparse matrix solver, and the mesh generation scheme is shown to lead to algorithms that can be implemented on inexpensive reduced instruction set computer (RISC) workstations with run times on the order of hours. An example of hyperthermia device simulation is presented which suggests that the finite element method is a practical alternative that rivals the impressive finite-difference time-domain (FDTD) computations that have appeared.

Current sheet applicator arrays for superficial hyperthermia of chestwall lesions

The current sheet applicator is an electromagnetic heating device whose size may be chosen virtually independent of frequency even though practical limitations may restrict it to VHF and UHF bands. In this paper we investigate absorbed power distributions in muscle tissue from current sheet applicators when used as elements of a planar array intended for superficial hyperthermic treatment of tumours. Advantages offered by current sheet applicators for tissue heating include compact size, a linear polarization of the induced electric field and relatively large heating area. It is shown that the effective field produced by a pair of these elements is continuous regardless of whether the common edges of the elements are perpendicular or parallel to the direction of impressed current. The feasibility of customizing the shape and size of the field is also illustrated. The absorbed power distribution patterns due to a coherently driven array operating around 434 MHz is relatively insensitive to phase variations of about 20 degrees but is sensitive to relative power level variations as low as 10%. Mutual coupling between array elements may be reduced to acceptable levels by incorporating suitable spacing between them. It is also demonstrated that there is good agreement between measurements of absorbed power distributions and predictions using the Gaussian beam model.

Comparison of numerical calculations with phantom experiments and clinical measurements

Three-dimensional models, while fundamentally desirable in hyperthermia treatment simulation, are only beginning to emerge and may take a number of years to perfect for routine clinical use. Two dimensional calculations, on the other hand, can be efficiently performed on today's inexpensive computer workstations; however, the accuracy of two-dimensional models in the pretreatment planning context is questionable. This paper investigates the ability of a general two-dimensional finite element model to predict power deposition patterns in phantoms and temperature distributions during actual clinical treatments. The experiments and simulations have been performed for an annular phased array (APA) operating at 70 MHz. Comparisons between model predictions and measurements show that quantitative agreement occurs in phantoms containing moderate complexities in heterogeneity, but that only qualitative agreement appears possible in clinical treatments. However, the results suggest that the lack of blood flow information may contribute as much, if not more, to the uncertainties in the clinical predictions than the two-dimensional nature of the model itself.

Theoretical quantification of the effects of plastic wall thickness on phantom measurements in electromagnetic hyperthermia

Phantom experiments are a staple of research and development in electromagnetic hyperthermia. Phantom containers and compartments are typically constructed from plastics which are readily available in a wide variety of thicknesses and material compositions. The perturbation effects of these plastics on the electric fields to be measured may be important, especially if one is trying to obtain quantitative results such as when comparing with a numerical model. This communication presents a theoretical investigation into the effects of plastic wall thickness on the computed electric field. Design curves are reported which aid in the selecting of an acceptable wall thickness given a maximum degree of wall perturbation that can be tolerated. Many other materials such as rubbers and polystyrenes also have electrical properties within the ranges considered herein; hence, the results should apply to a variety of commonly used phantom construction materials.

Optimization of the absorbed power distribution for an annular phased array hyperthermia system

One of the systems under investigation for producing hyperthermia noninvasively for treating deep-seated tumors is the annular phased array. This device consists of two rings of eight electromagnetic apertures that are placed concentrically about the long axis of the patient and radiate energy toward the center. Previous theoretical and clinical studies have concentrated primarily on systems where the amplitude and phase of the signal applied to each aperture were the same, and these studies have shown that the system is capable of depositing power deep within the patient. Nevertheless, in many situations the system was not capable of producing desirable temperature distributions in the tumor and normal tissue. In this paper we report on a 2-dimensional theoretical investigation where an optimization routine was used to select the amplitude and phases of each of eight apertures. The optimization procedure and resulting calculations were based on CT scans of patients with tumors. The electrical and thermal properties of the different organs and tissues were taken into account. The optimization routine tried to achieve uniform absorbed power in the tumor region with zero absorbed power outside. Using the optimized amplitudes and phases, the SAR (specific absorption rate, W/kg) was calculated for the array. The results show that in general the optimization procedure was successful in that the power deposited within the tumor volume was increased with less power deposited into normal tissue when compared to the equal amplitude and phase case. This SAR data was then used as the input to a program based on the bioheat transfer equation, which calculated the temperature distribution in the patient model for an assumed set of blood perfusion rates. Depending on the location, size of the tumor, and blood perfusion rates, the improvement in the percentage of the tumor brought to therapeutic temperature varied from 0% to as much as 80%.

Comparative theoretical performance for two types of regional hyperthermia systems

Regional hyperthermia systems have drawn attention because of their potential for depositing power noninvasively in deep-seated tumors. Two such systems that have received clinical attention because of their ability to deposit significant amounts of power in tissue are magnetic induction devices and annular phased array applicators. In this paper, theoretical calculations for the specific absorption rate (SAR) and the resulting temperature distributions for these systems are compared. The finite element method is used in the formulation of both the electromagnetic and thermal boundary value problems. Six detailed patient models based on CT-scan data from the pelvic, visceral, and thoracic regions are generated to simulate a variety of tumor locations. In general, the annular phased array deposited more power within the tumor and produced better temperature distributions than the magnetic induction device. However, the ratio of the maximum power absorbed by the tumor to the maximum power absorbed in normal tissue does not appear to be high enough for either device to heat significant portions of perfused tumors to therapeutic temperatures under a wide range of physiological conditions. The results contained herein should aid the physician in comparative treatment planning with existing regional hyperthermia systems.

Theoretical temperature distributions produced by an annular phased array-type system in CT-based patient models

Theoretical calculations for the specific absorption rate (SAR) and the resulting temperature distributions produced by an annular phased array (APA)-type system are made. The finite element numerical method is used in the formulation of both the electromagnetic (EM) and thermal boundary value problems. A number of detailed two-dimensional patient models based on CT-scan data from the pelvic, visceral, and thoracic regions are generated to simulate a variety of tumor locations and surrounding normal tissues. The SAR values from the EM solution are put into the bioheat transfer equation, and steady-state temperature distributions are calculated for a wide range of blood flow rates. Based on our theoretical modeling, the APA shows no preferential heating of superficial over deep-seated tumors. However, in most cases for all three regions of the human trunk only fair thermal profiles (therapeutic area near 60%) are obtained in tumors with little or no blood flow and poor temperature patterns (therapeutic area less than 50%) are found in tumors with moderate to high perfusion rates. These theoretical calculations should aid the clinician in the evaluation of the effectiveness of APA-type devices in heating tumors located in the trunk region.

Theoretical temperature profiles for concentric coil induction heating devices in a two-dimensional, axi-asymmetric, inhomogeneous patient model

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 and the temperature distributions were calculated for a wide range of blood flow rates. Based on the steady-state and transient results, our computer simulations predict poor therapeutic temperature profiles for tumors embedded deeply in the thorax and viscera. This heating technique appears to produce significant therapeutic volumes in superficial tumors located not greater than 7 cm in depth. These theoretical calculations should aid the clinician in the evaluation of induction heating devices for their effectiveness in heating deep-seated and superficial tumors.