Utility of treatment planning for thermochemotherapy treatment of nonmuscle invasive bladder carcinoma.

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.

Mathematical formulation and analysis of the nonlinear system reconstruction of the online image-guided adaptive control of hyperthermia.

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.

Effective learning strategies for real-time image-guided adaptive control of multiple-source hyperthermia applicators.

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.

Accuracy of real time noninvasive temperature measurements using magnetic resonance thermal imaging in patients treated for high grade extremity soft tissue sarcomas.

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.

Real-time MRI-guided hyperthermia treatment using a fast adaptive algorithm.

Magnetic resonance (MR) imaging is promising for monitoring and guiding hyperthermia treatments. The goal of this work is to investigate the stability of an algorithm for online MR thermal image guided steering and focusing of heat into the target volume. The control platform comprised a four-antenna mini-annular phased array (MAPA) applicator operating at 140 MHz (used for extremity sarcoma heating) and a GE Signa Excite 1.5 T MR system, both of which were driven by a control workstation. MR proton resonance frequency shift images acquired during heating were used to iteratively update a model of the heated object, starting with an initial finite element computed model estimate. At each iterative step, the current model was used to compute a focusing vector, which was then used to drive the next iteration, until convergence. Perturbation of the driving vector was used to prevent the process from stalling away from the desired focus. Experimental validation of the performance of the automatic treatment platform was conducted with two cylindrical phantom studies, one homogeneous and one muscle equivalent with tumor tissue (conductivity 50% higher) inserted, with initial focal spots being intentionally rotated 90 degrees and 50 degrees away from the desired focus, mimicking initial setup errors in applicator rotation. The integrated MR-HT treatment platform steered the focus of heating into the desired target volume in two quite different phantom tissue loads which model expected patient treatment configurations. For the homogeneous phantom test where the target was intentionally offset by 90 degrees rotation of the applicator, convergence to the proper phase focus in the target occurred after 16 iterations of the algorithm. For the more realistic test with a muscle equivalent phantom with tumor inserted with 50 degrees applicator displacement, only two iterations were necessary to steer the focus into the tumor target. Convergence improved the heating efficacy (the ratio of integral temperature in the tumor to integral temperature in normal tissue) by up to six-fold, compared to the first iteration. The integrated MR-HT treatment algorithm successfully steered the focus of heating into the desired target volume for both the simple homogeneous and the more challenging muscle equivalent phantom with tumor insert models of human extremity sarcomas after 16 and 2 iterations, correspondingly. The adaptive method for MR thermal image guided focal steering shows promise when tested in phantom experiments on a four-antenna phased array applicator.

The performance of a reduced-order adaptive controller when used in multi-antenna hyperthermia treatments with nonlinear temperature-dependent perfusion.

In large multi-antenna systems, adaptive controllers can aid in steering the heat focus toward the tumor. However, the large number of sources can greatly increase the steering time. Additionally, controller performance can be degraded due to changes in tissue perfusion which vary non-linearly with temperature, as well as with time and spatial position. The current work investigates whether a reduced-order controller with the assumption of piecewise constant perfusion is robust to temperature-dependent perfusion and achieves steering in a shorter time than required by a full-order controller. The reduced-order controller assumes that the optimal heating setting lies in a subspace spanned by the best heating vectors (virtual sources) of an initial, approximate, patient model. An initial, approximate, reduced-order model is iteratively updated by the controller, using feedback thermal images, until convergence of the heat focus to the tumor. Numerical tests were conducted in a patient model with a right lower leg sarcoma, heated in a 10-antenna cylindrical mini-annual phased array applicator operating at 150 MHz. A half-Gaussian model was used to simulate temperature-dependent perfusion. Simulated magnetic resonance temperature images were used as feedback at each iteration step. Robustness was validated for the controller, starting from four approximate initial models: (1) a 'standard' constant perfusion lower leg model ('standard' implies a model that exactly models the patient with the exception that perfusion is considered constant, i.e., not temperature dependent), (2) a model with electrical and thermal tissue properties varied from 50% higher to 50% lower than the standard model, (3) a simplified constant perfusion pure-muscle lower leg model with +/-50% deviated properties and (4) a standard model with the tumor position in the leg shifted by 1.5 cm. Convergence to the desired focus of heating in the tumor was achieved for all four simulated models. The controller accomplished satisfactory therapeutic outcomes: approximately 80% of the tumor was heated to temperatures 43 degrees C and approximately 93% was maintained at temperatures <41 degrees C. Compared to the controller without model reduction, a approximately 9-25 fold reduction in convergence time was accomplished using approximately 2-3 orthonormal virtual sources. In the situations tested, the controller was robust to the presence of temperature-dependent perfusion. The results of this work can help to lay the foundation for real-time thermal control of multi-antenna hyperthermia systems in clinical situations where perfusion can change rapidly with temperature.

Control time reduction using virtual source projection for treating a leg sarcoma with nonlinear perfusion.

PURPOSE: Blood perfusion is a well-known factor that complicates accurate control of heating during hyperthermia treatments of cancer. Since blood perfusion varies as a function of time, temperature and location, determination of appropriate power deposition pattern from multiple antenna array Hyperthermia systems and heterogeneous tissues is a difficult control problem. Therefore, we investigate the applicability of a real-time eigenvalue model reduction (virtual source - VS) reduced-order controller for hyperthermic treatments of tissue with nonlinearly varying perfusion. METHODS: We impose a piecewise linear approximation to a set of heat pulses, each consisting of a 1-min heat-up, followed by a 2-min cool-down. The controller is designed for feedback from magnetic resonance temperature images (MRTI) obtained after each iteration of heat pulses to adjust the projected optimal setting of antenna phase and magnitude for selective tumor heating. Simulated temperature patterns with additive Gaussian noise with a standard deviation of 1.0°C and zero mean were used as a surrogate for MRTI. Robustness tests were conducted numerically for a patient's right leg placed at the middle of a water bolus surrounded by a 10-antenna applicator driven at 150 MHz. Robustness tests included added discrepancies in perfusion, electrical and thermal properties, and patient model simplifications. RESULTS: The controller improved selective tumor heating after an average of 4-9 iterative adjustments of power and phase, and fulfilled satisfactory therapeutic outcomes with approximately 75% of tumor volumes heated to temperatures >43°C while maintaining about 93% of healthy tissue volume < 41°C. Adequate sarcoma heating was realized by using only 2 to 3 VSs rather than a much larger number of control signals for all 10 antennas, which reduced the convergence time to only 4 to 9% of the original value. CONCLUSIONS: Using a piecewise linear approximation to a set of heat pulses in a VS reduced-order controller, the proposed algorithm greatly improves the efficiency of hyperthermic treatment of leg sarcomas while accommodating practical nonlinear variation of tissue properties such as perfusion.

Fast temperature optimization of multi-source hyperthermia applicators with reduced-order modeling of 'virtual sources'.

The goal of this work is to build the foundation for facilitating real-time magnetic resonance image guided patient treatment for heating systems with a large number of physical sources (e.g. antennas). Achieving this goal requires knowledge of how the temperature distribution will be affected by changing each source individually, which requires time expenditure on the order of the square of the number of sources. To reduce computation time, we propose a model reduction approach that combines a smaller number of predefined source configurations (fewer than the number of actual sources) that are most likely to heat tumor. The source configurations consist of magnitude and phase source excitation values for each actual source and may be computed from a CT scan based plan or a simplified generic model of the corresponding patient anatomy. Each pre-calculated source configuration is considered a 'virtual source'. We assume that the actual best source settings can be represented effectively as weighted combinations of the virtual sources. In the context of optimization, each source configuration is treated equivalently to one physical source. This model reduction approach is tested on a patient upper-leg tumor model (with and without temperature-dependent perfusion), heated using a 140 MHz ten-antenna cylindrical mini-annular phased array. Numerical simulations demonstrate that using only a few pre-defined source configurations can achieve temperature distributions that are comparable to those from full optimizations using all physical sources. The method yields close to optimal temperature distributions when using source configurations determined from a simplified model of the tumor, even when tumor position is erroneously assumed to be approximately 2.0 cm away from the actual position as often happens in practical clinical application of pre-treatment planning. The method also appears to be robust under conditions of changing, nonlinear, temperature-dependent perfusion. The proposed approach of using virtual sources reduces the number of variables that must be optimized to achieve a tumor-focused temperature distribution, thereby reducing the calculation time required in real-time control applications to about 1/3 to 1/4 of that required for full optimization.

Online feedback focusing algorithm for hyperthermia cancer treatment.

PURPOSE: Magnetic resonance (MR) imaging is increasingly being utilized to visualize the 3D temperature distribution in patients during treatment with hyperthermia or thermal ablation therapy. The goal of this work is to lay the foundation for improving the localization of heat in tumors with an online focusing algorithm that uses MR images as feedback to iteratively steer and focus heat into the target. METHODS: The algorithm iteratively updates the model that quantifies the relationship between the source (antenna) settings and resulting tissue temperature distribution. At each step in the iterative process, optimal settings of power and relative phase of each antenna are computed to maximize averaged tumor temperature in the model. The MR-measured thermal distribution is then used to update/correct the model. This iterative procedure is repeated until convergence, i.e. until the model prediction and MR thermal image are in agreement. A human thigh tumor model heated in a 140 MHz four-antenna cylindrical mini-annular phased array is used for numerical validation of the proposed algorithm. Numerically simulated temperatures are used during the iterative process as surrogates for MR thermal images. Gaussian white noise with a standard deviation of 0.3 degrees C and zero mean is added to simulate MRI measurement uncertainty. The algorithm is validated for cases where the source settings for the first iteration are based on erroneous models: (1) tissue property variability, (2) patient position mismatch, (3) a simple idealized patient model built from CT-based actual geometry, and (4) antenna excitation uncertainty due to load dependent impedance mismatch and antenna cross-coupling. Choices of starting heating vector are also validated. RESULTS: The algorithm successfully steers and focuses a tumor when there is no antenna excitation uncertainty. Temperature is raised to > or = 43 degrees C for more than about 90% of tumor volume, accompanied by less than about 20% of normal tissue volume being raised to a temperature > or = 41 degrees C. However, when there is antenna excitation uncertainty, about 40% to 80% of normal tissue volume is raised to a temperature > or = 41 degrees C. No significant tumor heating improvement is observed in all simulations after about 25 iteration steps. CONCLUSIONS: A feedback control algorithm is presented and shown to be successful in iteratively improving the focus of tissue heating within a four-antenna cylindrical phased array hyperthermia applicator. This algorithm appears to be robust in the presence of errors in assumed tissue properties, including realistic deviations of tissue properties and patient position in applicator. Only moderate robustness was achieved in the presence of misaligned applicator/tumor positioning and antenna excitation errors resulting from load mismatch or antenna cross coupling.

Blood perfusion and thermal conduction effects in Gaussian beam, minimum time single-pulse thermal therapies.

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.