Optimal steady-state temperature distribution for a phased array hyperthermia system

Predicted SAR/temperature changes induced by phase-amplitude steering are minimally affected by uncertainties in tissue properties: a basis for robust on-line adaptive hyperthermia treatment planning

BACKGROUND

Reliability of absolute specific absorption rate (SAR)/temperature levels predicted by treatment planning is strongly affected by tissue parameter uncertainties. Therefore, regular re-optimization to suppress hot spots can accidentally induce new hot spots elsewhere. Adaptive planning methods to avoid this problem re-optimize with respect to the current predicted 3D-distribution. This strategy is robust if reliability of predicted SAR/temperature changes (i.e., increases/decreases) after phase-amplitude adjustments is minimally affected by parameter uncertainties; this work evaluated this robustness.

METHODS

We validated the basic concept in an inhomogeneous phantom, followed by a patient model. Uncertainties in electrical conductivity, permittivity and perfusion were mimicked by simulations using 100 random parameter samples from normal distributions. Reliability of predicted SAR/temperature increase/decrease after phase-amplitude adjustments was evaluated. Next, correlations between measured and simulated SAR and SAR changes were determined for phase settings evaluated at the treatment start for a treatment series. Finally, practical use in an adaptive workflow was illustrated.

RESULTS

Local SAR/temperature increases/decreases after phase-amplitude adjustments can be predicted accurately. For the phantom, the measured 28.5% SAR decrease was predicted accurately(28.5 ± 0.7%). In the patient model, predicted SAR/temperature changes were typically accurate within a few percent. For the treatment series, correlations between measured and simulated (relative) SAR changes were much better(R2=0.70-0.82) than for absolute SAR levels(R2=0.29). Predictions of steering effects during treatment corresponded qualitatively with measurements/observations.

CONCLUSION

Predictions of SAR/temperature increases/decreases induced by phase-amplitude steering are hardly affected by tissue parameter uncertainties. On-line adaptive planning based on predicted changes is thus robust to effectively support clinical steering strategies.

Fast Adaptive Temperature-Based Re-Optimization Strategies for On-Line Hot Spot Suppression during Locoregional Hyperthermia

Simple Summary

When treatment limiting hot spots occur during locoregional hyperthermia (i.e., heating tumors to 40–44 °C for ~1 h), system settings are adjusted based on experience. In this study, we developed and evaluated treatment planning with temperature-based re-optimization and compared the predicted effectiveness to clinically applied protocol/experience-based steering. Re-optimization times were typically ~10 s; sufficiently fast for on-line use. Effective hot spot suppression was predicted, while maintaining adequate tumor heating. Inducing new hot spots was avoided. Temperature-based re-optimization to suppress treatment limiting hot spots seemed feasible to match the effectiveness of long-term clinical experience and will be further evaluated in a clinical setting. When numerical algorithms are proven to match long-term experience, the overall treatment quality within hyperthermia centers can significantly improve. Implementing these strategies would then imply that treatments become less dependent on the experience of the center/operator.

Abstract

Background: Experience-based adjustments in phase-amplitude settings are applied to suppress treatment limiting hot spots that occur during locoregional hyperthermia for pelvic tumors. Treatment planning could help to further optimize treatments. The aim of this research was to develop temperature-based re-optimization strategies and compare the predicted effectiveness with clinically applied protocol/experience-based steering. Methods: This study evaluated 22 hot spot suppressions in 16 cervical cancer patients (mean age 67 ± 13 year). As a first step, all potential hot spot locations were represented by a spherical region, with a user-specified diameter. For fast and robust calculations, the hot spot temperature was represented by a user-specified percentage of the voxels with the largest heating potential (HPP). Re-optimization maximized tumor T90, with constraints to suppress the hot spot and avoid any significant increase in other regions. Potential hot spot region diameter and HPP were varied and objective functions with and without penalty terms to prevent and minimize temperature increase at other potential hot spot locations were evaluated. Predicted effectiveness was compared with clinically applied steering results. Results: All strategies showed effective hot spot suppression, without affecting tumor temperatures, similar to clinical steering. To avoid the risk of inducing new hot spots, HPP should not exceed 10%. Adding a penalty term to the objective function to minimize the temperature increase at other potential hot spot locations was most effective. Re-optimization times were typically ~10 s. Conclusion: Fast on-line re-optimization to suppress treatment limiting hot spots seems feasible to match effectiveness of ~30 years clinical experience and will be further evaluated in a clinical setting.

ESHO benchmarks for computational modeling and optimization in hyperthermia therapy

BACKGROUND

The success of cancer hyperthermia (HT) treatments is strongly dependent on the temperatures achieved in the tumor and healthy tissues as it correlates with treatment efficacy and safety, respectively. Hyperthermia treatment planning (HTP) simulations have become pivotal for treatment optimization due to the possibility for pretreatment planning, optimization and decision making, as well as real-time treatment guidance.

MATERIALS AND METHODS

The same computational methods deployed in HTP are also used for in silico studies. These are of great relevance for the development of new HT devices and treatment approaches. To aid this work, 3 D patient models have been recently developed and made available for the HT community. Unfortunately, there is no consensus regarding tissue properties, simulation settings, and benchmark applicators, which significantly influence the clinical relevance of computational outcomes.

RESULTS AND DISCUSSION

Herein, we propose a comprehensive set of applicator benchmarks, efficacy and safety optimization algorithms, simulation settings and clinical parameters, to establish benchmarks for method comparison and code verification, to provide guidance, and in view of the 2021 ESHO Grand Challenge (Details on the ESHO grand challenge on HTP will be provided at https://www.esho.info/).

CONCLUSION

We aim to establish guidelines to promote standardization within the hyperthermia community such that novel approaches can quickly prove their benefit as quickly as possible in clinically relevant simulation scenarios. This paper is primarily focused on radiofrequency and microwave hyperthermia but, since 3 D simulation studies on heating with ultrasound are now a reality, guidance as well as a benchmark for ultrasound-based hyperthermia are also included.

Regional deep hyperthermia: impact of observer variability in CT-based manual tissue segmentation on simulated temperature distribution

The aim of this study was to systematically investigate the influence of the inter- and intra-observer segmentation variation of tumors and organs at risk on the simulated temperature coverage of the target. CT scans of six patients with tumors in the pelvic region acquired for radiotherapy treatment planning were used for hyperthermia treatment planning. To study the effect of inter-observer variation, three observers manually segmented in the CT images of each patient the following structures: fat, muscle, bone and the bladder. The gross tumor volumes (GTV) were contoured by three radiation oncology residents and used as the hyperthermia target volumes. For intra-observer variation, one of the observers of each group contoured the structures of each patient three times with a time span of one week between the segmentations. Moreover, the impact of segmentation variations in organs at risk (OARs) between the three inter-observers was investigated on simulated temperature distributions using only one GTV. The spatial overlap between individual segmentations was assessed by the Dice similarity coefficient (DSC) and the mean surface distance (MSD). Additionally, the temperatures T90/T10 delivered to 90%/10% of the GTV, respectively, were assessed for each observer combination. The results of the segmentation similarity evaluation showed that the DSC of the inter-observer variation of fat, muscle, the bladder, bone and the target was 0.68  ±  0.12, 0.88  ±  0.05, 0.73  ±  0.14, 0.91  ±  0.04 and 0.64  ±  0.11, respectively. Similar results were found for the intra-observer variation. The MSD results were similar to the DSCs for both observer variations. A statistically significant difference (p  <  0.05) was found for T90 and T10 in the predicted target temperature due to the observer variability. The conclusion is that intra- and inter-observer variations have a significant impact on the temperature coverage of the target. Furthermore, OARs, such as bone and the bladder, may essentially influence the homogeneity of the simulated target temperature distribution.

Blind focusing of electromagnetic fields in hyperthermia exploiting target contrast variations

This paper suggests a novel approach to the blind focusing of the electromagnetic field for microwave hyperthermia. The idea is to induce a contrast variation in the target and to exploit this variation for the synthesis of the excitations of the antenna array employed for the focusing, by performing a differential scattering measurement. In particular, the excitation vector is set as the right singular vector associated with the largest singular value of the differential scattering matrix, obtained as difference of two scattering matrixes measured by the antenna array itself before and after the contrast change. As a result, the approach is computationally effective and totally blind, not requiring any a priori knowledge of the electric and geometric features of the region hosting the target, as well as of its spatial position with respect to the antenna array.

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.

Prospective treatment planning to improve locoregional hyperthermia for oesophageal cancer

BACKGROUND

In the Academic Medical Center (AMC) Amsterdam, locoregional hyperthermia for oesophageal tumours is applied using the 70 MHz AMC-4 phased array system. Due to the occurrence of treatment-limiting hot spots in normal tissue and systemic stress at high power, the thermal dose achieved in the tumour can be sub-optimal. The large number of degrees of freedom of the heating device, i.e. the amplitudes and phases of the antennae, makes it difficult to avoid treatment-limiting hot spots by intuitive amplitude/phase steering.

AIM

Prospective hyperthermia treatment planning combined with high resolution temperature-based optimization was applied to improve hyperthermia treatment of patients with oesophageal cancer.

METHODS

All hyperthermia treatments were performed with 'standard' clinical settings. Temperatures were measured systemically, at the location of the tumour and near the spinal cord, which is an organ at risk. For 16 patients numerically optimized settings were obtained from treatment planning with temperature-based optimization. Steady state tumour temperatures were maximized, subject to constraints to normal tissue temperatures. At the start of 48 hyperthermia treatments in these 16 patients temperature rise (DeltaT) measurements were performed by applying a short power pulse with the numerically optimized amplitude/phase settings, with the clinical settings and with mixed settings, i.e. numerically optimized amplitudes combined with clinical phases. The heating efficiency of the three settings was determined by the measured DeltaT values and the DeltaT-ratio between the DeltaT in the tumour (DeltaToes) and near the spinal cord (DeltaTcord). For a single patient the steady state temperature distribution was computed retrospectively for all three settings, since the temperature distributions may be quite different. To illustrate that the choice of the optimization strategy is decisive for the obtained settings, a numerical optimization on DeltaT-ratio was performed for this patient and the steady state temperature distribution for the obtained settings was computed.

RESULTS

A higher DeltaToes was measured with the mixed settings compared to the calculated and clinical settings; DeltaTcord was higher with the mixed settings compared to the clinical settings. The DeltaT-ratio was approximately 1.5 for all three settings. These results indicate that the most effective tumour heating can be achieved with the mixed settings. DeltaT is proportional to the Specific Absorption Rate (SAR) and a higher SAR results in a higher steady state temperature, which implies that mixed settings are likely to provide the most effective heating at steady state as well. The steady state temperature distributions for the clinical and mixed settings, computed for the single patient, showed some locations where temperatures exceeded the normal tissue constraints used in the optimization. This demonstrates that the numerical optimization did not prescribe the mixed settings, because it had to comply with the constraints set to the normal tissue temperatures. However, the predicted hot spots are not necessarily clinically relevant. Numerical optimization on DeltaT-ratio for this patient yielded a very high DeltaT-ratio ( approximately 380), albeit at the cost of excessive heating of normal tissue and lower steady state tumour temperatures compared to the conventional optimization.

CONCLUSION

Treatment planning can be valuable to improve hyperthermia treatments. A thorough discussion on clinically relevant objectives and constraints is essential.

High-resolution temperature-based optimization for hyperthermia treatment planning

In regional hyperthermia, optimization techniques are valuable in order to obtain amplitude/phase settings for the applicators to achieve maximal tumour heating without toxicity to normal tissue. We implemented a temperature-based optimization technique and maximized tumour temperature with constraints on normal tissue temperature to prevent hot spots. E-field distributions are the primary input for the optimization method. Due to computer limitations we are restricted to a resolution of 1 x 1 x 1 cm3 for E-field calculations, too low for reliable treatment planning. A major problem is the fact that hot spots at low-resolution (LR) do not always correspond to hot spots at high-resolution (HR), and vice versa. Thus, HR temperature-based optimization is necessary for adequate treatment planning and satisfactory results cannot be obtained with LR strategies. To obtain HR power density (PD) distributions from LR E-field calculations, a quasi-static zooming technique has been developed earlier at the UMC Utrecht. However, quasi-static zooming does not preserve phase information and therefore it does not provide the HR E-field information required for direct HR optimization. We combined quasi-static zooming with the optimization method to obtain a millimetre resolution temperature-based optimization strategy. First we performed a LR (1 cm) optimization and used the obtained settings to calculate the HR (2 mm) PD and corresponding HR temperature distribution. Next, we performed a HR optimization using an estimation of the new HR temperature distribution based on previous calculations. This estimation is based on the assumption that the HR and LR temperature distributions, though strongly different, respond in a similar way to amplitude/phase steering. To verify the newly obtained settings, we calculate the corresponding HR temperature distribution. This method was applied to several clinical situations and found to work very well. Deviations of this estimation method for the AMC-4 system were typically smaller than 0.2 degrees C in the volume of interest, which is accurate enough for treatment planning purposes.

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.

One-dimensional phased array with mechanical motion for conformal ultrasound hyperthermia

This paper investigates the feasibility of conformal heating for external ultrasound hyperthermia by using a phased array transducer with mechanical motion. In this system, a one-dimensional phased array is arranged on a shaft and moves along the shaft, while dynamically focusing on the planning target volume (PTV) with numerous focal spots. To prevent overheating in the intervening tissue between the skin and the PTV, the shaft and the phased array are rotated together to enlarge the acoustical window. With the purpose of conformal heating, the power deposition of the PTV is constructed by combinations of the focal spots and an iterative gradient descent method is then used to determine an optimal set of power weightings for the focal spots. Different tumour shapes are evaluated and the simulation results demonstrate that the volume percentage of the PTV with temperatures higher than 43 degrees C is over 95%. The overheating volume outside the PTV is less than 25% of the PTV. This method provides good conformal heating for external ultrasound hyperthermia. The concept of combining electrical focusing and mechanical motion has the advantages of both enlarging the acoustic window and providing dynamic focusing ability, which is essential for successful conformal heating.

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).

Engineering aspects of hyperthermia therapy

The continuing accrual of positive results in clinical cancer trials of adjunctive, synergistic hyperthermia therapy remains a strong motivation for the development of improved hyperthermia equipment and software. Indeed, the lack of needed engineering tools can be viewed as the major stumbling block to hyperthermia's effective clinical implementation. Developing clinically effective systems will be difficult, however, because (a) it requires solving several complex engineering problems, for which (b) setting appropriate design and evaluation goals is currently difficult owing to a lack of critical biological, physiological, and clinical knowledge, two tasks which must (c) be accomplished within a complicated social/political structure.

A fast algorithm to find optimal controls of multiantenna applicators in regional hyperthermia

The goal of regional hyperthermia is to heat up deeply located tumours to temperatures above 42 C while keeping the temperatures in normal tissues below tissue-dependent critical values. The aim of this paper is to describe and analyse functions which can be used for computing hyperthermia treatment plans in line with these criteria. All the functionals considered here can be optimized by efficient numerical methods. We started with the working hypothesis that maximizing the quotient of integral absorbed power inside the tumour and a weighted energy norm outside the tumour leads to clinically useful power distributions which also yield favourable temperature distributions. The presented methods have been implemented and tested with real patient data from the Charité Berlin. Campus Virchow-Klinikum. The results obtained by these fast routines are comparable with those obtained by relatively expensive global optimization techniques. Thus the described methods are very promising for online optimization in a hybrid system for regional hyperthermia where a fast response to MR-based information is important.

Impact of nonlinear heat transfer on temperature control in regional hyperthermia

We describe an optimization process specially designed for regional hyperthermia of deep-seated tumors in order to achieve desired steady-state temperature distributions. A nonlinear three-dimensional heat transfer model based on temperature-dependent blood perfusion is applied to predict the temperature. Using linearly implicit methods in time and adaptive multilevel finite elements in space, we are able to integrate efficiently the instationary nonlinear heat equation with high accuracy. Optimal heating is obtained by minimizing an integral objective function which measures the distance between desired and model predicted temperatures. A sequence of minima is calculated from successively improved constant-rate perfusion models employing a damped Newton method in an inner iteration. We compare temperature distributions for two individual patients calculated on coarse and fine spatial grids and present numerical results of optimizations for a Sigma 60 Applicator of the BSD 2000 Hyperthermia System.

Computational techniques for fast hyperthermia temperature optimization

Hyperthermia temperature optimization involves arriving at a temperature distribution which minimizes a stated goal function, the goal function having a biological basis in maximizing tumor cell kill while not exceeding normal tissue toxicity. This involves the computationally intensive process of multiple evaluations of the temperature goal function, requiring repeated evaluations of the power deposition and its corresponding temperature distribution. Two computational schemes are proposed to expedite the temperature optimization process: (1) temperature distribution evaluation by superpositioning precomputed distributions, and (2) using representative tissue groups (rather than every point in the domain) to evaluate the goal function. The application of these schemes is illustrated with a typical optimization problem, as applied to symmetric and asymmetric, heterogeneous models. Application of these schemes reduced the optimization time on a DEC Alpha 1000 4/266 (Alpha is a registered trademark of Digital Equipment Corporation.) from several h to min, with little difference in results. The computational schemes, though demonstrated in the context of electromagnetic hyperthermia, are generally applicable to other forms of nonionizing radiation employed in hyperthermia therapy.

Thermal dose optimization for ultrasound tissue ablation

A formal and general thermal dose optimisation method is developed and tested. Prior methods require brute force searches wherein the temperature and dose distributions must be computed at each iteration by solving the bioheat transfer equation (BHTE) numerically. This is extremely time-consuming and can only be used to compare a few prespecified strategies instead of obtaining a more general optimal result. With the method developed here, dose distribution can be calculated without solving the BHTE numerically. This can be done in a matter of a few minutes compared with many hours. Moreover, general thermal dose optimization can now be performed to find the optimal strength and location of each focus so that an optimal dose distribution is obtained while the specified constraint is satisfied. The algorithm developed here consists of a closed-form solution to the BHTE, a Gaussian model for parameterizing a temperature distribution created by a power deposition pattern, and a two-step optimization technique for obtaining the model parameters that optimize the thermal dose distribution. Several examples are given to demonstrate the effectiveness of the algorithm and its robustness under different initial conditions and under assumptions of different sizes of the target region and different numbers of foci. The algorithm developed here provides an efficient and effective tool for treatment planning in ultrasound tissue ablation.

Optimization of temperature distributions for regional hyperthermia based on a nonlinear heat transfer model

We describe an optimization process specially designed for regional hyperthermia of deep seated tumors in order to achieve desired steady-state temperature distributions. A nonlinear three-dimensional heat-transfer model based on temperature-dependent blood perfusion is applied to predict the temperature. Optimal heating is obtained by minimizing an integral object function which measures the distance between desired and model predicted temperatures. Sequential minima are calculated from successively improved constant-rate perfusion models employing a damped Newton method in an inner iteration. Numerical results for a Sigma 60 applicator are presented.

Optimization of the deposited power distribution inside a layered lossy medium irradiated by a coupled system of concentrically placed waveguide applicators

A method is proposed for controlling the deposited power distribution in a layered cylindrical lossy model, irradiated by a phased-array hyperthermia system consisting of four waveguide applicators. A rigorous electromagnetic model of the heated tissue, which takes into account coupling phenomena between system elements, is used for predicting the electric field at any point inside tissue. The relative amplitudes and relative phases of the array elements are optimized in order to attain desired specific absorption rate (SAR) distributions inside and outside malignant tissues. A constrained nonlinear optimization problem is solved by using the penalty function method and the resulting unconstrained minimization of the penalty function is carried out by the downhill simplex method. Two practical phased-array hyperthermia systems have been studied and numerical results are presented.

Minimax optimization-based inverse treatment planning for interstitial thermal therapy

The following work represents the development and evaluation of a minimax optimization-based inverse treatment planning approach for interstitial thermal therapy of cancer and benign disease. The goal is to determine a priori optimal applicator placements and power level settings to maintain the minimum tumour temperature, Tmin, and maximum normal tissue temperature, Tmax within a prescribed therapeutic temperature range. The temperature distribution is approximated by a finite element method (FEM) solution of a bioheat transfer equation on a nonuniform finite element mesh. Lower and upper therapeutic temperature thresholds are specified in the tumour and surrounding normal tissues. A constrained minimax optimization problem is formulated to determine optimal applicator positions and power level settings that minimize the maximum (rather than average) temperature errors in the target tumour region and surrounding normal tissues. The optimization problem is formulated for two general classes of interstitial heating applicators, those with and without a surface cooling mechanism. The viability and sensitivity of this approach is investigated in the two-dimensional setting for various tumour shapes and blood perfusion levels using surface-cooled and direct-coupled interstitial ultrasound applicator power deposition models. These preliminary results indicate the utility of this approach for meeting a prescribed Tmin/Tmax-based clinical objective criterion, and its potential for generating optimal treatment plans that can withstand variations or uncertainty in blood perfusion levels.

Simulation studies promote technological development of radiofrequency phased array hyperthermia

A treatment planning program package for radiofrequency hyperthermia has been developed. It consists of software modules for processing three-dimensional computerized tomography (CT) data sets, manual segmentation, generation of tetrahedral grids, numerical calculation and optimisation of three-dimensional E field distributions using a volume surface integral equation algorithm as well as temperature distributions using an adaptive multilevel finite-elements code, and graphical tools for simultaneous representation of CT data and simulation results. Heat treatments are limited by hot spots in healthy tissues caused by E field maxima at electrical interfaces (bone/muscle). In order to reduce or avoid hot spots suitable objective functions are derived from power deposition patterns and temperature distributions, and are utilised to optimise antenna parameters (phases, amplitudes). The simulation and optimisation tools have been applied to estimate the improvements that could be reached by upgrades of the clinically used SIGMA-60 applicator (consisting of a single ring of four antenna pairs). The investigated upgrades are increased number of antennas and channels (triple-ring of 3 x 8 antennas and variation of antenna inclination. Significant improvement of index temperatures (1-2 degrees C) is achieved by upgrading the single ring to a triple ring with free phase selection for every antenna or antenna pair. Antenna amplitudes and inclinations proved as less important parameters.