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Purpose: A recently completed Phase I clinical trial combined concurrent Mitomycin-C chemotherapy with deep regional heating using BSD-2000 Sigma-Ellipse applicator (BSD Corporation, Salt Lake City, UT, U.S.A.) for the treatment of nonmuscle invasive bladder cancer. This work presents a new treatment planning approach, and demonstrates potential impact of this approach on improvement of treatment quality., Methods: This study retrospectively analyzes a subset of five patients on the trial. For each treatment, expert operators selected "clinical-optimal" settings based on simple model calculation on the BSD-2000 control console. Computed tomography (CT) scans acquired prior to treatment were segmented to create finite element patient models for retrospective simulations with Sigma-HyperPlan (Dr. Sennewald Medizintechnik GmbH, Munchen, Germany). Since Sigma-HyperPlan does not account for the convective nature of heat transfer within a fluid filled bladder, an effective thermal conductivity for bladder was introduced. This effective thermal conductivity value was determined by comparing simulation results with clinical measurements of bladder and rectum temperatures. Regions of predicted high temperature in normal tissues were compared with patient complaints during treatment. Treatment results using "computed-optimal" settings from the planning system were compared with clinical results using clinical-optimal settings to evaluate potential of treatment improvement by reducing hot spot volume., Results: For all five patients, retrospective treatment planning indicated improved matches between simulated and measured bladder temperatures with increasing effective thermal conductivity. The differences were mostly within 1.3 °C when using an effective thermal conductivity value above 10 W/K/m. Changes in effective bladder thermal conductivity affected surrounding normal tissues within a distance of ∼1.5 cm from the bladder wall. Rectal temperature differences between simulation and measurement were large due to sensitivity to the sampling locations in rectum. The predicted bladder T90 correlated well with single-point bladder temperature measurement. Hot spot locations predicted by the simulation agreed qualitatively with patient complaints during treatment. Furthermore, comparison between the temperature distributions with clinical and computed-optimal settings demonstrated that the computed-optimal settings resulted in substantially reduced hot spot volumes., Conclusions: Determination of an effective thermal conductivity value for fluid filled bladder was essential for matching simulation and treatment temperatures. Prospectively planning patients using the effective thermal conductivity determined in this work can potentially improve treatment efficacy (compared to manual operator adjustments) by potentially lower discomfort from reduced hot spots in normal tissue.

Purpose: A nonlinear system reconstruction can theoretically provide timely system reconstruction when designing a real-time image-guided adaptive control for multisource heating for hyperthermia. This clinical need motivates an analysis of the essential mathematical characteristics and constraints of such an approach., Methods: The implicit function theorem (IFT), the Karush-Kuhn-Tucker (KKT) necessary condition of optimality, and the Tikhonov-Phillips regularization (TPR) were used to analyze and determine the requirements of the optimal system reconstruction. Two mutually exclusive generic approaches were analyzed to reconstruct the physical system: The traditional full reconstruction and the recently suggested partial reconstruction. Rigorous mathematical analysis based on IFT, KKT, and TPR was provided for all four possible nonlinear reconstructions: (1) Nonlinear noiseless full reconstruction, (2) nonlinear noisy full reconstruction, (3) nonlinear noiseless partial reconstruction, and (4) nonlinear noisy partial reconstruction, when a class of nonlinear formulations of system reconstruction is employed., Results: Effective numerical algorithms for solving each of the aforementioned four nonlinear reconstructions were introduced and formal derivations and analyses were provided. The analyses revealed the necessity of adding regularization when partial reconstruction is used. Regularization provides the theoretical support for one to uniquely reconstruct the optimal system. It also helps alleviate the negative influences of unavoidable measurement noise. Both theoretical analysis and numerical examples showed the importance of having a good initial guess for accomplishing nonlinear system reconstruction., Conclusions: Regularization is mandatory for partial reconstruction to make it well posed. The Tikhonov-Phillips regularized Gauss-Newton algorithm has nice theoretical performance for partial reconstruction of systems with and without noise. The Levenberg-Marquardt algorithm is a more robust algorithmic option compared to the Gauss-Newton algorithm for nonlinear full reconstruction. A severe limitation of nonlinear reconstruction is the time consuming calculations required for the derivatives of temperatures to unknowns. Developing a method of model reduction or implementing a parallel algorithm can resolve this. The results provided herein are applicable to hyperthermia with blood perfusion nonlinearly depending on temperature and in the presence of thermally significant blood vessels.

Purpose: This paper investigates overall theoretical requirements for reducing the times required for the iterative learning of a real-time image-guided adaptive control routine for multiple-source heat applicators, as used in hyperthermia and thermal ablative therapy for cancer., Methods: Methods for partial reconstruction of the physical system with and without model reduction to find solutions within a clinically practical timeframe were analyzed. A mathematical analysis based on the Fredholm alternative theorem (FAT) was used to compactly analyze the existence and uniqueness of the optimal heating vector under two fundamental situations: (1) noiseless partial reconstruction and (2) noisy partial reconstruction. These results were coupled with a method for further acceleration of the solution using virtual source (VS) model reduction. The matrix approximation theorem (MAT) was used to choose the optimal vectors spanning the reduced-order subspace to reduce the time for system reconstruction and to determine the associated approximation error. Numerical simulations of the adaptive control of hyperthermia using VS were also performed to test the predictions derived from the theoretical analysis. A thigh sarcoma patient model surrounded by a ten-antenna phased-array applicator was retained for this purpose. The impacts of the convective cooling from blood flow and the presence of sudden increase of perfusion in muscle and tumor were also simulated., Results: By FAT, partial system reconstruction directly conducted in the full space of the physical variables such as phases and magnitudes of the heat sources cannot guarantee reconstructing the optimal system to determine the global optimal setting of the heat sources. A remedy for this limitation is to conduct the partial reconstruction within a reduced-order subspace spanned by the first few maximum eigenvectors of the true system matrix. By MAT, this VS subspace is the optimal one when the goal is to maximize the average tumor temperature. When more than 6 sources present, the steps required for a nonlinear learning scheme is theoretically fewer than that of a linear one, however, finite number of iterative corrections is necessary for a single learning step of a nonlinear algorithm. Thus, the actual computational workload for a nonlinear algorithm is not necessarily less than that required by a linear algorithm., Conclusions: Based on the analysis presented herein, obtaining a unique global optimal heating vector for a multiple-source applicator within the constraints of real-time clinical hyperthermia treatments and thermal ablative therapies appears attainable using partial reconstruction with minimum norm least-squares method with supplemental equations. One way to supplement equations is the inclusion of a method of model reduction.

Purpose: To establish accuracy of real time noninvasive temperature measurements using magnetic resonance thermal imaging in patients treated for high grade extremity soft tissue sarcomas., Methods: Protocol patients with advanced extremity sarcomas were treated with external beam radiation therapy and hyperthermia. Invasive temperature measures were compared to noninvasive magnetic resonance thermal imaging (MRTI) at 1.5 T performed during hyperthermia. Volumetric temperature rise images were obtained using the proton resonance frequency shift (PRFS) technique during heating in a 140 MHz miniannular phased array applicator. MRTI temperature changes were compared to invasive measurements of temperature with a multisensor fiber optic probe inside a #15 g catheter in the tumor. Since the PRFS technique is sensitive to drifts in the primary imaging magnetic field, temperature change distributions were corrected automatically during treatment using temperature-stable reference materials to characterize field changes in 3D. The authors analyzed MRT images and compared, in evaluable treatments, MR-derived temperatures to invasive temperatures measured in extremity sarcomas. Small regions of interest (ROIs) were specified near each invasive sensor identified on MR images. Temperature changes in the interstitial sensors were compared to the corresponding ROI PRFS-based temperature changes over the entire treatment and over the steady-state period. Nonevaluable treatments (motion/imaging artifacts, noncorrectable drifts) were not included in the analysis., Results: The mean difference between MRTI and interstitial probe measurements was 0.91 degrees C for the entire heating time and 0.85 degrees C for the time at steady state. These values were obtained from both tumor and normal tissue ROIs. When the analysis is done on just the tumor ROIs, the mean difference for the whole power on time was 0.74 degrees C and during the period of steady state was 0.62 degrees C., Conclusions: The data show that for evaluable treatments, excellent correlation (deltaT < 1 degrees C) of MRTI-ROI and invasive measurements can be achieved, but that motion and other artifacts are still serious challenges that must be overcome in future work.

A previous analytical study has shown that the minimum obtainable treatment time for a single pulse that delivers a given thermal dose to a specified point at a specified time occurs when the temperature at that point is rapidly raised to its maximum allowable value. The present study extends that result by investigating the spatial distribution of thermal effects of a single Gaussian shaped focal zone pulse that reaches that maximum allowable temperature at the center point of the focal zone. Analytical solutions are obtained that separately include the effects of perfusion and conduction. This situation is analyzed for a conservative treatment strategy in which the desired thermal dose is delivered when the tumor cools down to basal conditions. The results show that for a specified thermal dose delivered by a spherical Gaussian beam with focal widths below approximately 4 mm, the maximum allowable temperature, the minimum obtainable treatment time, and the size of the treatment zone (as a percentage of the size of the Gaussian beam) are all independent of the tissue blood perfusion, and are only functions of the focal zone size. Conversely, for focal widths above approximately 20 cm, these results are independent of the focal width and are only functions of blood perfusion. Between these two sizes (where most practical treatments will occur, since single pulses with widths of <4 mm and >20 cm will be uncommon in practice) a transition zone exists in which both perfusion and conduction effects are important. Thus while it is possible to implement a truly perfusion-independent, single pulse thermal treatment by using focal widths of <4 mm, in practice many such pulses will be needed to treat most tumors. This is especially true since the nonlinear temperature/thermal dose relationship causes the width of the delivered dose distribution to be only approximately 25%-30% of the width of the focal zone. However, shorter overall treatment times can be obtained when multiple pulses are linked together by using larger focal zone sizes, but this gain in treatment time is accompanied by increased effects of perfusion, illustrating the conflict between attaining both perfusion-independence and minimal treatment time for multiple-pulse thermal treatments.

The purpose of this paper is to examine the optimal driving frequency and to configure the ultrasound energy deposition schema for a various size and location of breast tissues when a portion or the entire cylindrical ultrasound transducer is employed for breast hyperthermia treatments. This work employs a computer simulation program based on an ideal ultrasound power deposition from a cylindrical transducer. The ultrasound power within the breast is assumed to be exponentially attenuated according to the penetration depth of the ultrasound beam and a uniform absorption for the entire breast is also assumed. The distribution of the specific absorption rate (SAR) ratio is employed to determine the heating pattern of a set of given parameters. The control parameters considered are the ultrasound frequency in the breast tissue, the active portion of cylindrical transducer, and the shifting distance between the central axes of the breast and the transducer. The effect of the breast size on the SAR ratio is also considered. Simulation results demonstrate that the breast size, the ultrasound frequency in breast tissue, the shifting distance, and the active portion of the cylindrical transducer are the potential parameters for influencing the distribution of the SAR ratio. High frequencies should be used for the superficial heating treatments and the active portion of the transducer can be changed to obtain a region with an appropriate SAR ratio to cover the treatment region. Low frequencies are used for deep heating treatments and the region of the high SAR ratio can be moved by shifting the transducer and its pattern is varied with the transducer's active portion. The distribution of the SAR ratio indicates the domain of treatable tumor size and tumor depth for a given set of parameters (driving frequency, shifting distance and active portion of the transducer, as well as breast diameter). Findings of this study can be used to know whether or not the tumor is treatable as well as to select the optimal driving frequency and the appropriate active portion of the cylindrical transducer for a treatment, and hopefully to design an appropriate cylindrical ultrasound heating system for breast tumors.