Kung-Shan Cheng

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.

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°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 ≥43°C for more than about 90% of tumor volume, accompanied by less than about 20% of normal tissue volume being raised to a temperature ≥41°C. However, when there is antenna excitation uncertainty, about 40% to 80% of normal tissue volume is raised to a temperature ≥41°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.

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.

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.

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 patients 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.

Clinical utility of magnetic resonance thermal imaging (MRTI) for realtime guidance of deep hyperthermia

A critical need has emerged for volumetric thermometry to visualize 3D temperature distributions in real time during deep hyperthermia treatments used as an adjuvant to radiation or chemotherapy for cancer. For the current effort, magnetic resonance thermal imaging (MRTI) is used to measure 2D temperature rise distributions in four cross sections of large extremity soft tissue sarcomas during hyperthermia treatments. Novel hardware and software techniques are described which improve the signal to noise ratio of MR images, minimize motion artifact from circulating coupling fluids, and provide accurate high resolution volumetric thermal dosimetry. For the first 10 extremity sarcoma patients, the mean difference between MRTI region of interest and adjacent interstitial point measurements during the period of steady state temperature was 0.85°C. With 1min temporal resolution of measurements in four image planes, this noninvasive MRTI approach has demonstrated its utility for accurate monitoring and realtime steering of heat into tumors at depth in the body.

Clinical Utility of Magnetic Resonance Thermal Imaging (MRTI) For Realtime Guidance of Deep Hyperthermia

A critical need has emerged for volumetric thermometry to visualize 3D temperature distributions in real time during deep hyperthermia treatments used as an adjuvant to radiation or chemotherapy for cancer. For the current effort, magnetic resonance thermal imaging (MRTI) is used to measure 2D temperature rise distributions in four cross sections of large extremity soft tissue sarcomas during hyperthermia treatments. Novel hardware and software techniques are described which improve the signal to noise ratio of MR images, minimize motion artifact from circulating coupling fluids, and provide accurate high resolution volumetric thermal dosimetry. For the first 10 extremity sarcoma patients, the mean difference between MRTI region of interest and adjacent interstitial point measurements during the period of steady state temperature was 0.85°C. With 1min temporal resolution of measurements in four image planes, this noninvasive MRTI approach has demonstrated its utility for accurate monitoring and realtime steering of heat into tumors at depth in the body.

SU‐GG‐T‐366: Hyperthermia Treatment for a Patient with Two Shank Sarcomas Treated by a Fast Pre‐Treatment Optimization Method

Purpose:Cancerous cells are infiltrative and can invade neighborhood and/or distant body. While hyperthermia shows promising synergistic effects being used with radiation and/or chemotherapy, current microwave/radiofrequency power focusing techniques only focus one target at a time. Therefore, patients with multi‐sarcoma need to perform multi‐treatment in different days since a hyperthermia treatment requires maintaining tumor temperature >= 43°C for 60 minutes. Thus we investigate the feasibility of determining an optimal antenna setting that simultaneously elevates temperatures at two near‐by shank sarcomas so that patient comfort is enhanced and treatment times and costs are reduced. Method and Materials: A patient with two sarcomas was chosen to numerically validate our approach. Patient shank was surrounded by a 10‐antenna mini‐annual‐phased‐array (MAPA) operating at 138 MHz. A water bolus was placed between patient and MAPA to provide electric coupling and thermal cooling. A set of antenna settings were determined with a goal of maximizing averaged tumor temperature and were determined from the patient. The first few best antenna settings were chosen as virtual source (VS) basis vectors to span the reduced subspace. Magnitudes and phases of all 10 antennas were projected into this reduced subspace and then a set of temperature response functions for tumor and normal tissues were determined in this subspace. Numerical optimization was conducted to determine the optimal antenna setting that simultaneously elevates tumor temperatures and maintains safe normal tissue temperatures. Results: Results showed that we can use the 10‐antenna MAPA to simultaneously heat two sarcomas, and leave normal tissue undamaged. Furthermore, by comparing optimized temperatures when all 10 antennas were activated with that when only 4 VSs were used, we found these optimized temperatures are very comparable. Conclusion: Therefore, we presented an algorithm that allows physicians to treat patients with multi‐sarcoma and it also improves treatment planning efficiently.

SU‐GG‐T‐367: Fast Hyperthermia Temperature Optimization for Pelvic Carcinoma Patient Treated in Sigma‐Eye Applicator

Purpose: Though hyperthermia shows promising features being used with radiation and chemotherapy, it requires accurate spatial power focusing, which leads a workload proportional to square of number of antennas in an applicator. This motivates this investigation of model reduction method for pelvic‐carcinoma patient treated in Sigma‐Eye applicator. Method and Materials: A patient placed in the middle ring of this 100 MHz 3‐ring 12‐antenna applicator was used to validate our approach. A ‘similar’ patient with different thermal property values, perfusion values and was placed between the middle and low ring was used to determined virtual source (VS) basis vectors. A VS vector is a weighted combination of magnitudes and phases of 12 antennas and was determined to maximize averaged tumor temperature. Physical variables were projected to a reduced VS subspace spanned by a few VS vectors. Temperature response functions of tumor and normal tissues were determined in this reduced subspace and then used in temperature optimization iteration process. Results: By comparing the optimized temperature elevation distributions, we found it is indeed feasible to use a few chosen (best) VS basis vectors to optimally treat a pelvic carcinoma patient in Sigma‐Eye applicator; even when we determined those virtual source basis vectors from an existing “similar” patient. Conclusion: This success suggests a faster and easier pre‐treatment temperature optimization approach that relives workloads of physicians.

SU‐GG‐J‐164: Real‐Time Magnetic Resonance Imaging (MRI) Guidance and Thermal Modeling to Focus Hyperthermia Delivery

Purpose: Hyperthermia is an effective adjuvant modality for treatment of locally advanced cancer. However, focusing heat in the tumor using an external microwave applicator can be difficult, due to electromagnetic wave reflections at tissue interfaces. We present a methodology to steer heating towards the desired focus in real‐time, using MR thermal images for feedback. Method and Materials: The treatment control platform is based on repeated MR proton resonance frequency shift thermal imaging of the treatment volume over the course of the treatment. A cylindrical applicator with 4 independent pairs of dipole patch antennas (140MHz) is used as a heat source. The control process consists of iteratively constructing and updating a model for the heated object. At each iteration, the current model is employed to compute the optimal antenna settings (settings that the model predicts to focus heating in the target). These settings are applied to obtain the next thermal image, which is utilized in the next iteration to update the model. Thus, the algorithm progressively steers focusing while updating the model. We report on the convergence efficiency of the algorithm and importance of prior system knowledge (pretreatment simulations). Results: The experiments conducted on a cylindrical muscle‐equivalent phantom demonstrated that, for the 4‐antenna applicator, 16 iterations were sufficient to converge to the optimal thermal coverage of tumor. If prior knowledge was used, only 12 iterations were necessary to reach convergence from a starting focus that is positionally rotated 90° with respect to the desired focus. For a smaller positional rotation of 50°, 3 iterations were sufficient for convergence. The ratio of tumor to normal tissue heating after convergence improved by a factor of 3–6, compared to the initial ratio. Conclusion: Real‐time adaptive thermal modeling enables fast convergence to the optimal treatment of the patient and corrects for dynamic system changes.