2.1 Physical design of SC200 gantry

The design of the gantry structure depends on the optical design of the beam line. This means that the optical parameters of the gantry beam line should be carefully selected and optimized in order to design the most compact gantry. The position of horizontal and vertical planes is swapped due to rotation. This is required to ensure the same beam characteristics on both planes at the entrance. Moreover, the isocenter will not change with rotation in order to make the beam delivery of the gantry independent of the rotating angle of the gantry itself and, thus, simplify the design of the beam optics.

The paper presents a new optical design of the isocentric gantry, which is calculated with the software TRANSPORT. The principle of beam line inversion (BLI) is adopted to design the optics of the gantry beam according to the requirements on the isocenter beam. The initial conditions concern the shape of the beam and its energy: the shape is circular at the isocenter, with a full width at half maximum (FWHM) of 4–10 mm, and the energy varies in the range 70–200 MeV. The beam is deflected with three magnets (AMD3 90°, AMD2 60°, AMD1 60°) and focused by seven quadrupoles (QMD1-QMD7). The layout of the gantry beam line is shown in Fig. 1. The beam envelope of the first-order beam-optics calculation of the SC200 gantry is shown in Fig. 2. The main parameters of the gantry beam line are summarized in Table 1. Considering the proton beam energy and the maximum magnetic field that the magnets can reach, the bending radius of the gantry magnets is set to be 1.5 m. The edge angle is 30° for each bending magnet and the effective length of the quadrupole is 0.25 m.

Fig. 1Full-screen View

Layout of the SC200 gantry beam line.

Fig. 2Full-screen View

(Color online) Beam envelope of the gantry (first-order beam-optics calculation for the SC200 gantry). The curve in the upper (lower) part of the plot represents the vertical (horizontal) envelope. The dotted line indicates the 1%-dispersion trajectory.

Based on the optical design of the gantry beam line, the gantry of the SC200 PTF is designed taking into consideration the space of the treatment room and the construction cost. The main design element is the basic cylinder structure, which allows a more uniform stressing and a lower weight. The maximum and minimum diameters of the cylinder structure are 5000 mm and 4400 mm, respectively. The three-dimensional (3D) model of the gantry is shown in Fig. 3. Two support rings are installed on both ends of the gantry at a distance of 7850 mm between the two. The main support is a self-centering multi-wheels structure.

Fig. 3Full-screen View

(Color online) 3D model of the gantry. The system of global coordinates used is shown on the top-left corner of the figure.

Bonded yokes should be connected to the gantry. During the beam transport, the direction of the EM force remains unchanged against the structure of gantry, whereas its relative direction and self-gravity change with the rotation of the gantry. Hence, the integrated load changes synchronously.

2.2 Electromagnetic-Structure Coupling Analysis

As far as the PTF concerns, various beam energies are needed to ensure an effective radiation of tumors located at different depths. On account of the fact that the rotation radius is constant, the field of dipoles should change according to the beam energy. The correlation between the field intensity and the beam energy is described by equation (1). The higher the beam energy, the higher the magnetic field needed to maintain a constant radius. Therefore, as to the EM force analysis, it is necessary to focus only on the maximum input currents, which are summarized in Table 2. The seven quadrupoles are classified by magnetic field gradient (the threshold is 12 T/m) into two groups. Quadrupoles of the same group adopt the same mechanical structure.

With consideration of the magnet design and beam motion, the direction of the input current is specific for each magnet. All the magnets are analyzed separately for EM force coupling. In order to map the EM force consistently, the global coordinate system of the analysis model must be the same in both Maxwell and ANSYS Workbench simulation environments. The total force is shown in purple in Fig. 4. As can be seen, the EM force of the beam line magnets is mainly reflected in the x and z directions of the dipoles AMD-3, AMD-2 and AMD-1, with an intensity of 50.97 kN, 49.29 kN, and 49.18 kN, respectively.

Fig. 4Full-screen View

(Color online) EM force of beam line magnets.

Given the complex structure of the nozzle, an alternative model is adopted. The simplified model consists of a skeleton, scan magnets, an ionization chamber (IC) and an outer support plate for the nozzle, whose stiffness and weight are almost the same as the real nozzle. The distance between the end of the last bending magnet and the isocenter is 2850 mm, including the 2650-mm nozzle length and the 200-mm air path, which are both shown in Fig. 1.

The 90° dipole and the 60° dipoles have a weight of 13 t and 6.5 t, respectively. Quadrupoles of the first and second group have a weight of 0.5 t and 0.8 t, respectively. The total weight of the gantry is 130 t. The weight ratio can reduce the impact of magnets weight on the gantry deformation. Therefore, the deformation of the gantry at different positions can be more uniform and controllable.

In order to simplify the analysis, the following key gantry angles are selected: 0°, ±45°, ±90°, ±135°, 180°. The gantry shown in Fig. 3 is at 0⁰. Fixed constraints have been applied to both ends of each support wheel. Two load steps are adopted to analyze the impact of the self-gravity and the EM force. The total deformation after load step two at 0° is shown in Fig. 5. The maximum deformation occurs in the middle position of the gantry, which is 0.26 mm. The maximum equivalent stress, which occurs in the contact position between the support ring and the support wheel, is equal to 47.79 MPa. Fig. 6 shows the maximum deformation of two load steps at the selected gantry angles. The maximum deformation always occurs in correspondence of the position of the 90° dipole. The deformation is symmetrical with respect to the x-z plane and it results to be less than 1 mm for all runs.

Fig. 5Full-screen View

(Color online) Total deformation of the gantry at 0° after load step two.

Fig. 6Full-screen View

(Color online) Maximum deformation of gantry at selected angles (square symbols represent the results after load step 1 and circle symbols represent the results after load step 2).

3.1 Method one: based on the nozzle installation

After understanding the deformation of the nozzle structure and the beam trajectory, we can calculate the optical path coming out of the nozzle. Theoretically, the isocenter is the intersection between the axis of the nozzle and the rotating axis of the gantry. Due to the deformation of the gantry and the nozzle, the actual isocenter is a region in space whose shape can be defined as the path of a point that is on the central axis of the beam delivery system and at a constant distance from the target (or scatterer), as the gantry rotates through its entire range of motions. Therefore, the isocenter size cannot be obtained directly.

To determine the size of the isocenter, the deformation data of the points A and B of the nozzle, as indicated in Fig. 1, are obtained directly. Such two points are on the axis of the nozzle. The distance between the point A and the isocenter is 2850 mm, whereas the distance between the point B and the isocenter is 200 mm. When the beam comes out of the nozzle from point B, it arrives at the practical isocenter through the same distance along the original direction of the motion at any gantry angle. Given this, the optical path coming out of the nozzle may be calculated to obtain the practical coordinate value of the isocenter in the global coordinate system.

3.2 Method two: based on the optical path after nozzle

The requirement of having the nozzle on the mechanical deformation of the gantry is essential for the gantry design. The scanning system and the ICs are placed on a rigid subplate, which maintains the relationship between magnets and ICs. Given the complexity of the nozzle system, the nozzle can be assumed to be perfectly rigid. Therefore, we can confine the attention on the location of the subplate relative to the rest of the gantry and look at the effects of the offsets in various axes. Figure 7 shows a scheme of a scan magnet deflecting a beam and an IC rigidly connected to the magnet. The chamber is represented with a deliberately exaggerated shift with respect to the beam path defined by the gantry, which is assumed to be perfect.

Fig. 7Full-screen View

Scheme of the nozzle system: (a) normal condition; (b) shift in the z direction; (c) shift in the x(y) direction; (d) rotation in the x-z(y-z) plane.

In all cases, the actual deflection of the beam is hardly affected, but the positions measured by the ionization chamber. By comparing the case (a) with the case (b) in Fig. 7, it can be observed that the shift in the z direction has a negligible effect on the beam line because the deflection angles are small. The shift in the x(y) direction brings the IC to measure the beam in the wrong position, even though the deflection in the magnet remains unchanged. The beam lines B and D pass through different positions of the IC. The position of the beam is wrongly measured when the x-z (y-z) plane is deflected; a deflection that results in a shift in the x(y) direction.

The requirement of rigidity imposed on the mounting of the nozzle is no worse than the same requirement imposed on other transfer line magnets on the gantry. Given that a typical requirement for spot placement accuracy at the isocenter plane is ±0.5 mm (pure mechanical accuracy), and a typical demagnification is about 1.6, the scan system subplate should be maintained in a position relative to the nominal beam trajectory that has to be better than 0.3 mm in x and y. The rotation in the planes x-z and y-z should be kept below about 0.3 mrad. The safe factor is set equal to 1.5. The requirements on the installation plate are expressed in equation (2). In this case, the local coordinate system is considered.

The rotation angle in the x-z plane is calculated with equation (3), where $z_{\max }$ and $z_{\min }$ represent the maximum and minimum deformation in the z direction, respectively; $l_{\text{x}}$ and $l_{\text{y}}$($l_{\text{x}}$= 1020mm, $l_{\text{y}}$= 1100mm) are the dimensions of the nozzle installation plate on the gantry in the x and y directions, respectively.

Assuming that the nozzle is perfectly rigid, we can get the equivalent isocenter deformation from the deformation and the rotation of the nozzle installation plate on the gantry. To achieve this, the relations expressed by equation (4) have to be used.

Here, $x_{\text{iso\_equi}}$,$y_{\text{iso\_equi}}$ and $z_{\text{iso\_equi}}$ are the equivalent isocenter deformations in the x, y and z directions, respectively. $\theta (xz)$ and $\theta (yz)$can be obtained from Eqs. (2) and (3). $l$ is the distance between point A and the isocenter.

4.1 Results

As to method one, the isocenter deformation is obtained by calculating the optical path coming out of the nozzle. The results are shown in Fig. 8. The optical path after the nozzle (200-mm long) is shown in Fig. 9.

Fig. 8Full-screen View

(Color online) Isocenter deviation obtained with method one (*-1 indicates the load step 1 and *-2 indicates the load step 2).

Fig. 9Full-screen View

(Color online) Optical path after the nozzle at selected gantry angles: (a) the middle point indicates the practical isocenter, whereas the peripheral points indicate the point B at certain selected gantry angles; (b) the practical isocenter in critical boundary.

The nozzle has a cantilever structure and, due to its own weight, the practical isocenter moves downward. The y-direction deviation in the vicinity of ±90° is exactly the opposite in the global coordinate system. As we can see from Fig. 8, only the x-direction deviation is affected by the EM force.

In general, the isocenter deviation in the x and y directions is less than 0.33 mm (considering a safety factor of 0.5–1.5) at selected gantry angles and the maximum linear distance between the theoretical and practical isocenter is 0.39 mm. The variation of the maximum deformation between two loads steps is 0.05 mm, which means that the EM force does not have a great impact on the isocenter deviation.

As to method two, the equivalent isocenter deformation can be obtained from the deformation data (deformation and rotation) of the installation subplate of the nozzle, which is shown in Fig. 10. In this case, the maximum deformation changes according to a regular pattern and it is symmetrically distributed along the 0° position. The rotation angle of the nozzle installation plate on the gantry is shown in Fig. 11. The maximum rotation angle is less than 0.1 mrad.

Fig. 10Full-screen View

(Color online) Technical parameters of the nozzle installation plate on the gantry: maximum deformation in the x and y directions (*-1 indicates the load step 1 and *-2 indicates the load step 2).

Fig. 11Full-screen View

(Color online) Technical parameters of the nozzle installation plate nozzle on the gantry: maximum plate rotation of the x-z and y-z plates (*-1 indicates the load step 1 and *-2 indicates the load step 2)

Starting from the results shown in Fig. 10 and Fig. 11, we can obtain $x_{\text{iso\_equi}}$,$y_{\text{iso\_equi}}$ and $z_{\text{iso\_equi}}$by using Eq. (4). It is worth to note that the relationship between the rotation and deformation directions of the nozzle installation plate, and the equivalent isocenter deformation, is converted into global coordinates for a consistent comparison with that obtained with method one. The result of such comparison is shown in Fig. 12

Fig. 12Full-screen View

(Color online) Comparison between the isocenter deformations obtained with methods one and two (*-1 indicates the load step 1 and *-2 indicates the load step 2).

As shown in Fig. 12, the difference between the isocenter deformations obtained with the two methods is quite small. Therefore, it can be neglected. In a practical application context this means that the isocenter is a point in space and it is difficult to determine its deformation directly. Thus, according to the results shown above, we can mount deformation-monitoring equipment on the nozzle installation plate and calculate the isocenter deformation by exploiting the monitoring data. Such method is applicable to realize real-time monitoring of the isocenter deformation.