Calculation of absorbed power in tissue for various hyperthermia devices.

Recently, there has been increased interest in the use of hyperthermia (temperatures, 42 to 45 degrees) as an adjuvant modality to radiation therapy or chemotherapy for the treatment of cancer. This paper discusses the use of the finite element method as a technique for calculating the power deposited per unit volume of tissue for two regional-type hyperthermia devices. The two types of devices investigated are inductive concentric coils and annular phased arrays. The mathematical basis for the finite element method and its advantages when dealing with problems involving irregular boundaries and nonhomogeneous tissue are reviewed. Specific examples are shown for the calculations of the electromagnetic fields and the resulting absorbed power density. Furthermore, it is shown how the basic finite element formulation for the electromagnetic problem can be extended to solving the temperature distribution problem. Temperature distributions for both types of devices are illustrated. Finally, the limitations of the finite element method are reviewed, and possible implications of the specific results for the efficacy of regional devices are raised.

Temperature distributions from interstitial rf electrode hyperthermia systems: theoretical predictions.

In recent years, there has been increased interest in the use of hyperthermia as an adjuvant modality to radiation and chemotherapy in the treatment of cancer. One of the more promising techniques is the application of an rf voltage to an array of electrodes inserted directly into the tumor. The electrodes are usually small, hollow stainless steel needles that are inserted as the first step in a brachytherapy procedure. By applying a voltage between the needles, an rf current is induced in the tissue, resulting in joule heating. In this paper, we calculate numerically the temperature distributions for an array of such needles. In our model we assume a two-dimensional problem, i.e. infinitely long needles, and a homogeneous medium. Blood flow effects are included in the calculation. The results show that for low blood perfusion rates, e.g., on the order of 3 ml/100 gm X min, very smooth temperature distributions result, and the electrodes can be spaced fairly far apart. However, for blood flow rates on the order of 20 ml/100 gm X min the temperature distributions are not smooth, and there are hot spots around the electrodes and cool regions between them. However, if the electrodes are spaced about 1 cm apart and the voltages are adjusted to optimize the temperature distribution then reasonably good results should be achievable. The equation is solved using a finite difference technique. By applying the superpostion principle, we are able to introduce a procedure which substantially reduces the amount of core storage required and results in reasonably efficient run times on a moderate size mini-computer.

A theoretical comparison of the temperature distributions produced by three interstitial hyperthermia systems.

Three interstitial hyperthermia systems were compared on the basis of their abilities to heat tumors: ferromagnetic seeds, microwave antennas, and rf electrode needles. The theoretical calculations were performed using two-dimensional tumor models containing static tissue and electrical properties and various blood flow patterns. Basic assumptions were kept the same to permit a meaningful comparison of the different systems. Power deposition patterns were calculated based on the appropriate theoretical expressions. The bioheat transfer equation was solved using a finite element method. Temperature distributions were calculated for four 1 or 2 mm diameter implants on the corners of 1, 2, and 3 cm squares. The tumor was assumed to be circular with a diameter 1 cm longer than the diagonal of each square. Three blood flow models were considered: homogeneous, nonhomogeneous, and concentric annulus perfusion models. The blood flow ranged from 0 to 100 ml/100 g/min with the ratio of tumor/normal tissue blood flow ranging from 0 to 40. A Hyperthermia Equipment Performance (HEP) rating was used as a criterion for comparing the temperature distributions from the various cases examined. As expected, the higher HEP ratings were generally produced by decreasing the spacing between the implants and/or lower blood perfusion rates. Under the conditions of this study, the microwave antennas were able to adequately heat a larger number of cases to therapeutic temperatures than either of the other two modalities.

Three-dimensional theoretical temperature distributions produced by 915 MHz dipole antenna arrays with varying insertion depths in muscle tissue.

Interstitial microwave antenna array hyperthermia (IMAAH) systems are currently being used in the treatment of cancer. The insertion depth of an interstitial microwave antenna, defined as the length of the antenna from the tip to the point of insertion in tissue, affects its ability to produce uniform power deposition patterns in tumor volumes. The effect of varying insertion depths on the ability of an IMAAH system to heat two theoretical tumor models was examined. Four dipole microwave antennas were implanted in a 2 x 2 cm array and driven at 915 MHz in muscle tissue. The explicit power deposition patterns were calculated for each insertion depth using known theory. The bioheat transfer equation was solved for the 3-dimensional steady-state temperature distributions in cylindrical and ellipsoidal tumor models using a finite element method. Homogeneous and nonhomogeneous blood flow models were considered. As a basis of comparison of the various temperature distributions, the volume of tumor heated to greater than or equal to 43 degrees C was calculated. Under the conditions of this study, the insertion depth was shown to have a significant effect on the ability of an IMAAH system to heat the tumor volumes. A sharp decrease in the percentage of tumor volume heated to greater than or equal to 43 degrees C was seen for insertion depths between 7.8 and 14.6 cm. At an insertion depth of 11.7 cm (3/4 lambda) there was virtually no heating of the tumor. Regions of elevated power occurred outside of the desired treatment volume, stressing the importance of adequate thermometry techniques and demonstrating the need for hyperthermia treatment planning prior to implantation of an antenna array. Plots of the power deposition patterns and the corresponding temperatures produced in the diagonal plane of the antenna arrays are present.

Absorbed power deposition for various insertion depths for 915 MHz interstitial dipole antenna arrays: experiment versus theory.

Dipole antennas are commonly used in interstitial clinical hyperthermia treatments because of their compatibility with brachytherapy techniques and their good power deposition patterns when used in arrays. For accurate treatment planning, however, there must be a comprehensive knowledge base to predict the power deposition patterns when insertion depth is a non-resonant length. This is especially true for insertion depths that result in significant power deposition outside of the antenna junction plane and presumably outside of the tumor volume. A computer controlled measurement system was used with a muscle equivalent phantom to make measurements of specific absorption rate (SAR) or absorbed power per unit mass of tissue at 598 points in a plane. The diagonal plane was the measurement plane of choice because it characterized the SAR profiles at the array center as well as areas in the proximity of the antennas. Dartmouth dipole antennas were used (0.9 mm O.D.) in brachytherapy catheters with inner catheters (2.2 mm O.D./1.2 mm I.D.). The resonant half-wavelength of this dipole antenna/catheter combination is 7.8 cm. A choke modification of the dipole was also investigated. Four antennas were used in a boxlike configuration with 2.0 cm separation. Insertion depths of 5.9, 7.8, 9.8, 12.7, 15.6 and 17.6 cm were used. The hA subsection (junction to tip) was held constant at 3.9 cm. Plots were made of the experimental SAR data normalized to the maximum SAR measured in the plane. Theoretical plots were calculated in the same plane for each of the insertion depths. SAR comparisons were also made longitudinally along the central axis of the array and through the antenna junctions in the diagonal plane for resonant half-wavelength insertion depth. Experimental results verified theoretical predictions of the existence of a secondary hot-spot in the center of the array, but outside of the antenna junction plane and approximately a quarter-wavelength from the insertion point. This secondary hot-spot appears for all insertion depths greater than 10 cm. At longer insertion depths approaching a full wavelength, however, this secondary peak is not dominant. Choke antennas demonstrated a solution to the problem of shifting SAR patterns with varying insertion depths by restricting the active length of the antenna.

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.

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%.

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.

Brain hyperthermia: I. Interstitial microwave antenna array techniques--the Dartmouth experience.

PURPOSE: Microwave antennas of various designs were inserted into arrays of nylon catheters implanted in brain tumors with the goal of raising temperatures throughout the target volume to 43.0 degrees C. METHODS AND MATERIALS: All antennas were flexible, and included dipole, choke dipole, modified dipole, and helical designs driven at 915 or 2450 MHz. Antennas were tested in brain-equivalent phantom in arrays. Phase shifting and phase rotation techniques were incorporated into the treatment system to steer power in the tumor, assisted by a treatment planning computer that predicted power deposition patterns and temperature distributions. Choke antennas were designed and tested to reduce a dependence of the central power location on depth of insertion into tissue. Temperature data analysis used only central and orthogonal axes mapping data measured at 2.0 mm intervals. RESULTS: A total of 23 patients were treated, using from one to six microwave antennas. Minimum tumor temperatures, averaged over the 60 min treatment, ranged from 37.2-44.3 degrees C (mean 40.0 degrees C) and maximum average tumor temperatures ranged from 46.5-60.1 degrees C (mean 49.1 degrees C). The percentage of all measured temperatures reaching therapeutic levels (> or = 43.0 degrees C) was 70.9. T90, the temperature at which 90% of all measured temperatures equaled or exceeded, was 40.8 degrees C, and T50 was 44.2 degrees C. CONCLUSION: Patient data analysis showed that the array of four dipole antennas spaced 2.0 cm apart were capable of heating a volume of 5.9 cm (along the central array axis) x 2.8 cm x 2.8 cm.

Experimental brain hyperthermia: techniques for heat delivery and thermometry.

An experimental canine brain model was developed to assess the effects of hyperthermia for a range of time and temperature endpoints, delivered within a specified distance of an interstitial microwave antenna in normal brain. The target temperature location was defined radially at 5.0 or 7.5 mm from the microwave source at the longitudinal location of maximum heating along the antenna in the left cerebral cortex. Temperatures were measured with fiberoptic probes in a coronal plane at this location in an orthogonal catheter at 1.0 mm intervals. Six antennas were evaluated, including dipole, modified dipole, and four shorted helical antennas with coil lengths from 0.5 to 3.9 cm. Antenna performance evaluated in tissue equivalent phantom by adjusting frequency at a fixed insertion depth of 7.8 cm or adjusting insertion depth at 915 MHz showed dipoles to be much more sensitive to insertion depth and frequency change than helical antennas. Specific absorption rate (SAR) was measured in a brain/skull phantom and isoSAR contours were plotted. In vivo temperature studies were also used to evaluate antenna performance in large and small canine brain tissues. A helical antenna with a 2.0 cm coil length driven at 915 MHz was chosen for the beagle experiments because of tip heating characteristics, well-localized heating along the coil length, and heating pattern appropriate to the smaller beagle cranial vault. Verification of lesion dimensions in 3-D was obtained by orthogonal MRI scans and histology to document the desired heat effect, which was to obtain an imagable lesion with well-defined blood-brain-barrier breakdown and necrotic zones. The desired lesion size was between 1.5 to 2.5 cm diameter radially, in the coronal plane with the greatest diameter.

Thermal conduction effects associated with temperature measurements in proximity to radiofrequency electrodes and microwave antennas.

The smearing effects due to thermal conduction along various, nonenergized, interstitial devices were quantified in a flow cell-thermal step gradient. An insulated cylindrical flow cell with a high (ca 45 degrees C, 1.12 cm i.d., 1.6 cm o.d.) temperature region surrounded by a low (ca 37 degrees C) temperature region was used to compare temperature profiles measured with a thermocouple sensor inside a Stanford radiofrequency (RF) hyperthermia/brachytherapy catheter, a BSD instrumented microwave (MW) antenna (i.e., thermistor integrated into a dipole antenna) and a Dartmouth MW antenna with a juxtaposed optical sensor. Two parameters were used to quantify the thermal smearing of each interstitial device in the flow cell: (a) the maximum temperature difference (MTD) and (b) the full- width- half-maximum (FWHM) of the high temperature region. The "true" temperature maximum (45.4 degrees C) and distribution (FWHM = 1.65 +/- 0.06 cm) were measured with an optical sensor. These data indicate that the BSD instrumented MW antenna significantly smeared the true temperature profile (MTD = 2.7 degrees C, FWHM = 2.1 cm), as did the Dartmouth MW antenna (MTD = 1.5 degrees C, FWHM = 1.7 cm). The Stanford RF catheter, when insulated, resulted in minimal smearing (MTD = 0.3 degrees C, FWHM = 1.9 cm). Moreover, when the insulation was removed so the RF electrode was exposed to the thermal step gradient, smearing was again minimal (MTD = 0.3 degrees C, FWHM = 1.9 cm).

Intraoperative interstitial microwave-induced hyperthermia and brachytherapy.

Intra-operative placement of 11-gauge nylon catheters into deep-seated unresectable tumors for interstitial brachytherapy permits localized heating of tumors (hyperthermia) using microwave (915 MHz) antennas which are inserted into these catheters. Four preliminary cases are described where epithelial tumors at various sites were implanted with an antenna array and heated for 1 hour, both before and after the iridium-192 brachytherapy. Temperatures were monitored in catheters required for the appropriate radiation dosimetry but not required for the interstitial microwave antenna array hyperthermia (IMAAH) system. Additional thermometry was obtained using nonperturbed fiberoptic thermometry probes inserted into the catheters' housing antennas. No significant complications, such as bleeding or infection, were observed. This approach to cancer therapy is shown to be feasible and it produces controlled, localized hyperthermia, with temperatures of 50 degrees C or more in tumors. This technique may offer a therapeutic option for pelvic, intra-abdominal and head and neck tumors.

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.

Mechanism of obstruction of closed-wound suction tubing.

The mechanism of obstruction of closed-wound drainage tubing was investigated by means of coagulation tests performed on wound drainage fluid and by examination of the contents of the tubes after their removal. Although clotting is commonly thought to be responsible for the obstruction, the wound drainage fluid was found to be essentially incoagulable and little fibrin was evident within the tubes. By contrast, bits of tissue were frequently found within the tubes, and these frequently virtually occluded the lumen. This observation, that tissue fragments are responsible for tube obstruction, permits a rational approach to the solution of this problem. For example, meticulous wound flushing and irrigation, or perhaps tubing of different design, might lead to a reduced incidence of tube failure.

Theoretical temperature distributions for solenoidal-type hyperthermia systems.

One type of system proposed for producing hyperthermia for cancer therapy of deep-seated tumors consists of a cylindrical conducting coil (solenoid) in which the patient (or a limb of the patient) is placed. The current in the conducting coil creates an alternating magnetic field inside the patient, which induces eddy currents in the tissue. The eddy currents deposit power and hence produce heating. In this paper, steady-state temperature profiles are calculated analytically, assuming a homogeneous one-dimensional model which includes blood perfusion. Numerical methods are used to calculate the temperature distributions as a function of time for this homogeneous model and to calculate the temperature profiles when there are radial variations in tissue parameters including blood flow. Based on these computer simulations, it would appear that in most cases a solenoid-type hyperthermia system will not be able to provide deep-seated heating in the abdomen or thorax, but should be able to raise temperatures to therapeutic levels to about 6 cm depth in the abdomen and in the muscle layer in the thorax.

Mathematical model of conventional tomography.

A Fourier decomposition approach is used to study the imaging properties of conventional tomography. Spatial frequency response curves (MTFs) are calculated for both linear and axial transverse tomography. These curves depend on the product of the spatial frequency of the sinusoidal density variations in thin layers parallel to the tomographic plane and the distance between such layers and the tomographic plane. Based on the spatial frequency response curves, a quantitative definition of tomographic layer thickness is given. Furthermore, the spatial frequency response curves suggest that unattenuated low-frequency information from outside the tomographic layer limits the resolution in conventional tomograms and that high-pass spatial filtering of the image may substantially improve the diagnostic quality of tomographic images, particularly in the identification of boundaries.

Linearizing mechanisms in conventional tomographic imaging.

Implicit in the concept of conventional tomography and in any attempt to characterize the tomographic process by a modulation transfer function is the assumption that the tomographic process is linear. A Fourier decomposition approach and an analysis of nonlinear contributions to the integrated tomographic image intensity are used in this paper to establish the validity of this assumption and to determine the mechanisms by which the tomographic process is effectively linearized.

Some aspects of optimization of an invasive microwave antenna for local hyperthermia treatment of cancer.

Hyperthermia has emerged as a promising alternative or adjunct to other forms of cancer therapy. In order to utilize hyperthermia in very localized volumes immersed in regions of vital normal tissue, an invasive microwave coaxial monopole antenna has been developed. An experimental approach has been taken to characterize and optimize the electromagnetic properties and heating capabilities of bare and insulated antennas imbedded in tissue equivalent phantoms and dog brain. Four methods have been used to visualize the thermal profiles of the microwave probes: the liquid crystal technique, the gelatin technique, and the direct measurement of temperature with thermistor probes in phantom and dog brain. Among the parameters studied are: antenna impedance, insertion depth, antenna insulation (dielectric constant and thickness), shaft insulation, and frequency.

Interstitial thermoradiotherapy.

The more recent engineering and clinical aspects of interstitial hyperthermia are reviewed. The advantages and difficulties of microwave, radiofrequency, and ferromagnetic seeds are evaluated and some future directions for improvements are outlined.

Extracranial application of the frameless stereotactic operating microscope: experience with lumbar spine.

The frameless stereotactic operating microscope has expanded the potential application of modern stereotaxis to procedures outside of the intracranial compartment by removing the constraint of a rigid frame. We studied seven patients all of whom had a history, examination, and imaging studies consistent with lumbosacral spinal pathology for which they subsequently underwent surgery with the operating microscope. The ability of the frameless stereotactic system with preoperative computed tomography data to locate the level of the lesion as well as define the boundary of the spinal pathology intraoperatively was assessed. In parallel with this application of the frameless system, we analyzed the relationship between the lumbar intervertebral disc spaces (L3-L4, L4-L5, L5-S1) and skin surface fiducials using lateral radiographs. In seven patients with extracranial cases (six herniated lumbar discs and one lumbar spondylolysis with Grade I spondylolisthesis) who underwent operations by this system, the accuracy of the digitization component of the system with respect to localization of an independent test fiducial was 3.28 mm (SD, 0.61). The accuracy of the entire system in locating the independent fiducial within the viewing plane was 6.05 mm (SD, 4.04). Disc space localization had a far greater error of 28.81 mm (SD, 7.49). There was no consistent pattern to the magnitude or direction of the displacement of the lumbar intervertebral discs with respect to the fiducial markers in the sagittal plane. Although accuracy at the level of the fiducial plane was similar to that of intracranial applications, paraspinal tissue and vertebral column deformations rendered poorer accuracy with deeper structures.