A method of MRI-based thermal modelling for a RF phased array

Parallel transmission RF pulse design with strict temperature constraints

RF safety in parallel transmission (pTx) is generally ensured by imposing specific absorption rate (SAR) limits during pTx RF pulse design. There is increasing interest in using temperature to ensure safety in MRI. In this work, we present a local temperature correlation matrix formalism and apply it to impose strict constraints on maximum absolute temperature in pTx RF pulse design for head and hip regions. Electromagnetic field simulations were performed on the head and hip of virtual body models. Temperature correlation matrices were calculated for four different exposure durations ranging between 6 and 24 min using simulated fields and body-specific constants. Parallel transmission RF pulses were designed using either SAR or temperature constraints, and compared with each other and unconstrained RF pulse design in terms of excitation fidelity and safety. The use of temperature correlation matrices resulted in better excitation fidelity compared with the use of SAR in parallel transmission RF pulse design (for the 6 min exposure period, 8.8% versus 21.0% for the head and 28.0% versus 32.2% for the hip region). As RF exposure duration increases (from 6 min to 24 min), the benefit of using temperature correlation matrices on RF pulse design diminishes. However, the safety of the subject is always guaranteed (the maximum temperature was equal to 39°C). This trend was observed in both head and hip regions, where the perfusion rates are very different.

Predicting long-term temperature increase for time-dependent SAR levels with a single short-term temperature response

PURPOSE

Present a novel method for rapid prediction of temperature in vivo for a series of pulse sequences with differing levels and distributions of specific energy absorption rate (SAR).

THEORY AND METHODS

After the temperature response to a brief period of heating is characterized, a rapid estimate of temperature during a series of periods at different heating levels is made using a linear heat equation and impulse-response (IR) concepts. Here the initial characterization and long-term prediction for a complete spine exam are made with the Pennes' bioheat equation where, at first, core body temperature is allowed to increase and local perfusion is not. Then corrections through time allowing variation in local perfusion are introduced.

RESULTS

The fast IR-based method predicted maximum temperature increase within 1% of that with a full finite difference simulation, but required less than 3.5% of the computation time. Even higher accelerations are possible depending on the time step size chosen, with loss in temporal resolution. Correction for temperature-dependent perfusion requires negligible additional time and can be adjusted to be more or less conservative than the corresponding finite difference simulation.

CONCLUSION

With appropriate methods, it is possible to rapidly predict temperature increase throughout the body for actual MR examinations.

Real-time microwave imaging of differential temperature for thermal therapy monitoring

A microwave imaging system for real-time 3-D imaging of differential temperature has been developed for the monitoring and feedback of thermal therapy systems. Design parameters are constrained by features of a prototype-focused microwave thermal therapy system for the breast, operating at 915 MHz. Real-time imaging is accomplished with a precomputed linear inverse scattering solution combined with continuous vector network analyzer (VNA) measurements of a 36-antenna, HFSS-modeled, cylindrical cavity. Volumetric images of differential change of dielectric constant due to temperature are formed with a refresh rate as fast as 1 frame/s and 1 (°)C resolution. Procedures for data segmentation and postprocessed S-parameter error-correction are developed. Antenna pair VNA calibration is accelerated by using the cavity as the unknown thru standard. The device is tested on water targets and a simple breast phantom. Differentially heated targets are successfully imaged in cluttered environments. The rate of change of scattering contrast magnitude correlates 1:1 with target temperature.

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.

Time-reversal focusing in microwave hyperthermia for deep-seated tumors

A fast beam-forming method for hyperthermia treatment of deep-seated tumors is described and verified. The approach is based on the time-reversal characteristics of Maxwell equations. The basic principle of the method is coupling of the electromagnetic modeling of the system with the actual application. In this modeling the wavefront of the source is propagated through a patient-specific model from a virtual antenna placed in the tumor of the model. The simulated radiated field is then captured using a computer model of the surrounding antenna system. The acquired amplitudes and phases are then used in the real antenna system. The effectiveness of this procedure is demonstrated by calculating the power absorption distribution using FDTD electromagnetic simulations of a realistic 2D breast model as well as a 2D neck model. Several design parameters, i.e. number of antennas, operating frequency and dimensions, have been evaluated by performance indicators. The promising results suggest that the development of this technique is pursued further.

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.

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 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.

Analysis of factors important for transurethral ultrasound prostate heating using MR temperature feedback

The feasibility of using MR thermometry for temperature feedback to control a transurethral ultrasound heating applicator with planar transducers was investigated. The sensitivity of a temperature-based feedback algorithm to spatial (control point area, slice thickness, angular alignment) and non-spatial (imaging time, temperature uncertainty) parameters was evaluated through numerical simulations. The angular alignment of the control point with the ultrasound beam was an important parameter affecting the average spatial error in heat delivery. The other spatial parameters were less influential, thus providing an opportunity to reduce spatial resolution for increased SNR in the MR imaging. The update time was the most important non-spatial parameter determining the performance of the control algorithm. Combined non-spatial and spatial parameters achieved acceptable performance with a voxel size of 3 mm x 3 mm, a 10 mm slice thickness and a 5 s update time. Temperature uncertainty of up to 2 degrees C had little effect on the performance of the control algorithm but did reduce the average error slightly due to a systematic, noise-induced overestimation of the boundary temperature. These simulations imply that MR thermometry performed on clinical 1.5 T imaging systems is of sufficient quality for use as thermal feedback for conformal prostate thermal therapy with transurethral ultrasound heating applicators incorporating planar transducers.

Effects of coil dimensions and field polarization on RF heating inside a head phantom

Deterioration of radiofrequency (RF) inhomogeneity with increasing static magnetic field in magnetic resonance imaging (MRI) is one of the fundamental challenges preventing their clinical rendition and posing safety hazards. Variation in RF coil designs could help redistribute RF energy absorption over the imaged object. This work is intended to determine experimentally the difference in RF heating produced within a human head phantom by in situ measurement of RF inhomogeneity as a function of coil design utilized at 8 T. The heating patterns of 1/4 wavelength (long) and 1/8 wavelength 11-cm (short) transverse electromagnetic (TEM) coils loaded with a homogeneous human head phantom at 340 MHz were evaluated. In addition, different transmit/receive (T/R) configurations were used in search for the possibility of "hot-spot" formation. Fluoroptic thermometry was used to measure temperatures in multiple positions in a head phantom made of ground turkey breast for RF powers corresponding to a specific absorption rate (SAR) of 4.0 W/kg for 10 min. Numerical simulations were performed to study the general RF power deposition patterns in phantoms at 340 MHz including the effects of field polarization. The temperature increases varied from 0 to 0.8 degrees C for the long RF coil, while the short RF coil produced a maximum temperature change of 0.5 degrees C. Similar to ultra high-field electromagnetic simulations, these measurements revealed low peripheral and high deep-tissue heating at 8 T. The findings indicated that the largest temperature changes for both cases were less than 1 degrees C. While these results showed an increase in localized heating due to RF pulses at 8 T, they highlight that RF inhomogeneity could be redistributed using different RF coil designs through which the hot spots could be made cooler.

A temperature-based feedback control system for electromagnetic phased-array hyperthermia: theory and simulation

A hybrid proportional-integral-in-time and cost-minimizing-in-space feedback control system for electromagnetic, deep regional hyperthermia is proposed. The unique features of this controller are that (1) it uses temperature, not specific absorption rate, as the criterion for selecting the relative phases and amplitudes with which to drive the electromagnetic phased-array used for hyperthermia and (2) it requires on-line computations that are all deterministic in duration. The former feature, in addition to optimizing the treatment directly on the basis of a clinically relevant quantity, also allows the controller to sense and react to time- and temperature-dependent changes in local blood perfusion rates and other factors that can significantly impact the temperature distribution quality of the delivered treatment. The latter feature makes it feasible to implement the scheme on-line in a real-time feedback control loop. This is in sharp contrast to other temperature optimization techniques proposed in the literature that generally involve an iterative approximation that cannot be guaranteed to terminate in a fixed amount of computational time. An example of its application is presented to illustrate the properties and demonstrate the capability of the controller to sense and compensate for local, time-dependent changes in blood perfusion rates.

Optimization of electromagnetic phased-arrays for hyperthermia via magnetic resonance temperature estimation

A technique for the optimization of electromagnetic annular phased arrays (APAs) for therapeutic hyperthermia has been developed and implemented. The controllable inputs are the amplitudes and phases of the driving signals of each element of the array. Magnetic resonance imaging (MRI) is used to estimate noninvasively the temperature distribution based on the temperature dependence of the proton resonance frequency (PRF). A parametric model of the dynamics that couple the control inputs to the resultant temperature elevations is developed based on physical considerations. The unknown parameters of this model are estimated during a pretreatment identification phase and can be continuously updated as new measurement data become available. Based on the parametric model, a controller automatically chooses optimal phases and amplitudes of the driving signals of the APA. An advantage of this approach to optimizing the APA is that no a priori information is required, eliminating the need for patient-specific computational modeling and optimization. Additionally, this approach represents a first step toward employing temperature feedback to make the optimization of the APA robust with respect to modeling errors and physiological changes. The ability of the controller to choose therapeutically beneficial driving amplitudes and phases is demonstrated via simulation. Experimental results are presented which demonstrate the ability of the controller to choose optimal phases for the APA using only information from magnetic resonance thermometry (MRT).