Precise magnetic field control of the scanning magnets for the APTRON beam delivery system

Precise magnetic field control of the scanning magnets for the APTRON beam delivery system 1 2 first-author 1 1 1 corresp Corresponding author: zhaozhentang@sinap.ac.cn Corresponding author: zhaozhentang@sinap.ac.cn zhaozhentang@sinap.ac.cn Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China University of Chinese Academy of Sciences, Beijing 100049, China University of Chinese Academy of Sciences, Beijing 100049, China A design for precise scanning magnetic field control for the beam delivery system of the Shanghai Advanced Proton Therapy Facility (APTRON) is presented in this paper. With a novel feedforward algorithm to compensate for magnet hysteresis, the scanning magnetic field can be controlled to within a precision of ±2.5 G. The main advantage of the proposed feedforward algorithm is that the average settling time is shorter compared with that of a conventional feedback algorithm with acceptable tolerance. Proton therapy Scanning magnet Hysteresis Feedforward control. 1 INTRODUCTION 1 Proton beams have been widely used in cancer therapy for the past few decades. The Shanghai Advanced Proton Therapy Facility (APTRON) is the first Chinese-developed, hospital-based proton therapy facility, and it is under construction at the time of writing [ 1 1 ]. The beam delivery system is one of the key systems in a proton therapy facility. Its function is to achieve the prescribed dose rate and three-dimensional dose distribution. Beam delivery systems commonly use a spot-scanning technique, which is also implemented in the APTRON beam delivery system. The distinct advantages of a spot-scanning beam delivery system are its lack of patient-specific hardware, precise three-dimensional conformal dose distribution, and excellent distal dose fall-off performance. 2 THE APTRON BEAM DELIVERY SYSTEM 1 A schematic diagram of the spot-scanning beam delivery system is shown in Fig. 1 Fig. 1 . Two orthogonal scanning magnets (SMU and SMV) are used to control the irradiation position of the proton beam. A photo of the SMU scanning magnet is shown in Fig. 2 Fig. 2 . The main design parameters of the scanning magnets are presented in Table 1 Table 1 . 1 1  Parameters 1 1 SMU 1 1 SMV 1 1 Deflection angle (mrad) 1 1 ±69.7  1 1 ±62.0  1 1 SAD (m) 1 1 2.87  1 1 2.42  1 1 Pole length (m) 1 1 0.205 1 1 0.230  1 1 Magnet length (m) 1 1 0.309  1 1 0.334  1 1 Magnet gap (mm) 1 1 30  1 1 109 1 1 Number of coil turns 1 1 48 1 1 64 1 1 Maximum field strength (T) 1 1 0.799  1 1 0.634  The workflow of the spot-scanning beam delivery system during the irradiation process is as follows: (1) The beam is moved to the prescribed position. (2) The proton beam is turned on. (3) The proton beam is turned off when the prescribed particle number has been reached. (4) The beam is moved to the next position. The transition time for moving the beam is part of the overall irradiation time. Therefore, the transition time should be as short as possible to achieve a high dose rate. In order to realize a high-accuracy three-dimensional dose distribution, the maximum error in the iso-center of the beam position should be within ±0.07 mm and the corresponding maximum error in the magnetic field strength should be within ±2.5 G. 3 HYSTERESIS EFFECT OF THE SCANNING MAGNETS 1 Magnetic hysteresis is the main factor that influences the accuracy of the scanning magnetic field. Hysteresis can be divided into rate-dependent hysteresis and rate-independent hysteresis. Rate-dependent hysteresis involves a dynamic response to changes in the magnetic field. Figure 3 Figure 3 shows the step response of the scanning magnet. When the input current of the scanning magnet changed by 5% of the maximum, the settling time of the magnetic field was less than 2 ms. The magnetic hysteresis loop is shown in Fig. 4 Fig. 4 , which illustrates the properties of rate-independent hysteresis. Following an investigation of ferromagnetic hysteresis loops, Kuhnen summarized the following rules for rate-independent hysteresis [ 2 2 ]: · Any curve C 1 emanating from a turning point A of the output–input trajectory is uniquely determined by the coordinate of A. · If any point B on the curve C 1 becomes a new turning point, then the curve C 2 originating at B leads back to the point A. · If the curve C 2 continues beyond the point A, then it coincides with the continuation of the curve C that led to the point A before the C 1 –C 2 cycle was traversed. Typical feedforward control strategies are a neural network control [ 3 3 - 5 5 3-5 ], Prandtl–Ishlinskii (PI) control [ 6 6 ], and generalized PI (GPI) control [ 7 7 - 11 11 7-11 ]. However, PI and GPI control are too complex to be realized in real-time calculation, which is necessary for control of the scanning magnetic field in the spot-scanning beam delivery system. 4 FEEDFORWARD CONTROL OF THE SCANNING MAGNETS 1 For a conventional feedback system, the magnet hysteresis is compensated for by the feedback loop. However, for a feedforward system, the magnetic hysteresis should be precisely modeled in order to achieve the required accuracy for the magnetic field strength. Another consideration in developing the hysteresis model is that the model calculation should be as simple as possible to meet the needs of real-time control. 4.1 A simplified model for rate-independent hysteresis 2 According to Madelung’s rules, any curve emanating from a turning point is uniquely determined by the coordinates of the turning point. As shown in Fig. 5 Fig. 5 , a bundle of curves may be recorded. The turning point is defined as the top point of the hysteresis loops (at the point of the arrow). The path (curve C 2 or C 5 ) from a starting point (the blue triangle) to a set point (the green square) is uniquely determined by the starting point. Because hysteresis loops are multi-valued functions, the curves for the increasing current and for the decreasing current are different and are recorded separately (as shown in Figs. 5(a) and (b) Figs. 5(a) and (b) ). 4.2 Feedforward control algorithm 2 The proposed feedforward control algorithm is based on the above simplified hysteresis model. Suppose that the initial values of the current magnetic field strength and the excitation current are B ini and I ini , respectively, the corresponding hysteresis curve is C , and the target magnetic field strength is B set , related like so: <math id="M1"><mrow><mi>C</mi><mo>:</mo><mi>B</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>I</mi><mo>)</mo></mrow><mo>.</mo></mrow></math> The set value of the excitation current I set is uniquely determined by the target magnetic field strength B set , and can be calculated by solving the following equation: <math id="M2"><mrow><msub><mi>B</mi><mrow><mtext>set</mtext></mrow></msub><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mrow><msub><mi>I</mi><mrow><mtext>set</mtext></mrow></msub></mrow><mo>)</mo></mrow><mo>.</mo></mrow></math> Only a limited number of curves were recorded for the sake of practicality. If the starting point ( I ini , B ini ) was not on any of these curves, then the closest curve was selected. All curves were fitted by piecewise functions and a linear interpolation method was implemented. To ensure a monotonic relationship between the excitation current and the magnetic field strength, overshoot of the scanning magnet’s power supply was avoided. In order to cover the entire region of possible starting points and to ensure the accuracy of the magnetic field strength, the excitation current at the ends of all the curves was set to the maximum current ± I max , and the distance between two adjacent curves at any given excitation current was within ±2.5 G. The input current shown in Fig. 6 Fig. 6 is: <math id="M3"><mrow><mi>I</mi><mo>=</mo><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><msub><mi>I</mi><mrow><mtext>ini</mtext></mrow></msub><mo>+</mo><mi>Δ</mi><mi>I</mi><mo>⋅</mo><mi>i</mi></mrow></mtd><mtd><mrow><mtext>(ascending curve)</mtext></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>I</mi><mrow><mtext>ini</mtext></mrow></msub><mo>−</mo><mi>Δ</mi><mi>I</mi><mo>⋅</mo><mi>i</mi></mrow></mtd><mtd><mrow><mtext>(decending curve)</mtext></mrow></mtd></mtr></mtable></mrow></mrow><mo>,</mo></mrow></math> where I ini is the initial excitation current, Δ I is the step-size of the change in current, and i is the sequence number of each measurement point. The hysteresis curves with the linear part subtracted are illustrated in Fig. 7 Fig. 7 . 5 EXPERIMENTAL RESULTS 1 The feedforward algorithm was tested using a benchmark of 100 random setting points for the magnetic field strength, ranging between − B max and + B max . The testing result is shown in Fig. 8 Fig. 8 . The maximum error and the mean squared error were 2.45 G and 0.60 G, respectively. The major source of control error was the distance between the adjacent recorded curves, the measurement accuracy of the magnetic field strength, and the reproducibility and stability of the scanning magnet’s power supply. The accuracy of the scanning magnetic field for the conventional feedback algorithm [ 3 3 ] is shown in Fig. 9 Fig. 9 . Among the 100 random setting points, 79 points need two iterations, 18 points need three iterations, and 3 points need four iterations. The accuracy of the feedback algorithm is considerably better than that of the feedforward algorithm; however, if the number of iterations is larger than two, the settling time of the scanning magnetic field is too large and the prescribed dose rate cannot be achieved. 6 DISCUSSION 1 From the comparison of the results of the feedforward and feedback control algorithms, we can see that the desired control precision of the magnetic field strength can be achieved through both algorithms. However, the average settling time of the proposed feedforward control algorithms is 2.2 times shorter than that of the conventional feedback algorithm. Because both algorithms can otherwise satisfy the control precision, the feedforward algorithm is preferred. 7 CONCLUSION 1 This paper proposed a novel feedforward control algorithm to achieve precise magnetic field control of the scanning magnets for the spot-scanning beam delivery system in the Shanghai Advanced Proton Therapy Facility (APTRON). 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Struct . 23 , 125017 ( 2014 ). doi: 10.1088/0964-1726/23/12/125017 http://doi.org/10.1088/0964-1726/23/12/125017 Modeling and inverse compensation of hysteresis in vanadium dioxide using an extended generalized Prandtl-Ishlinskii model We would like to thank Dr. Rui Li and Dr. Qing-Song Tan of the power supply group, and, Dr. Lian-Hua Ou-Yang and Dr. Bo-Lei Jia of the magnet group for their support. 10.1007/s41365-017-0324-6 This work was supported by the Youth Innovation Promotion Association CAS (No. 2016238). 2017-06-20 2017-08-21 2017-09-07 2017-11-16 2017-12-01 2022-08-18 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2017 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-017-0324-6 http://dx.doi.org/10.1007/s41365-017-0324-6 . 2017 Nuclear Science and Techniques 12 28