JP2012183283A - Rotating action verification system, rotating action verification method, program, and recording medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a system and a method for verifying rotating actions of rotating parts such as a gantry, a collimator, and a treatment bed of a radiotherapy unit.SOLUTION: The rotating action verification system includes an acceleration sensor 6 which is a sensor which can be fastened to the rotating parts in the radiotherapy unit, includes a detection means capable of detecting the acceleration rate and the angular velocity in the three axial directions including X, Y and Z intersecting each other at right angles, and includes a transmitter capable of transmitting data detected by the detection means, a receiver 8 receiving the data transmitted from the transmitter of the acceleration sensor 6, analysis software 9 computing the rotational path data of the unit on the basis of the data received by the receiver 8, and a computer 10 equipped with the analysis software 9.

Description

  The present invention relates to a rotation operation verification system and method for a rotating part such as a gantry, a collimator, and a treatment bed of a radiotherapy apparatus. More specifically, the present invention relates to an acceleration sensor or an angular velocity sensor in addition to the rotation part, and a rotating part. The present invention relates to a system and a method for calculating and verifying the stability of the rotational speed and the rotational trajectory by acquiring information such as acceleration.

  External radiotherapy (hereinafter referred to as radiotherapy) is a treatment aimed at shrinking and destroying lesions by irradiating tumors and malignant neoplasms (cancer, etc.) generated by an accelerator from outside the body. Is the law. In recent years, with the rise in the incidence of cancer and the westernization of cancer types, radiation therapy has become widespread, and the number of radiotherapy apparatuses has exceeded 800 units as of 2010 and is increasing year by year. In recent years, the irradiation method is not only from a fixed direction, but also from multiple directions toward the lesion (multi-portal irradiation), and by focusing the radiation on the lesion target, normal on the patient's skin surface outside the target and around the lesion Methods are used to reduce the dose to the tissue. There are several types of radiation therapy devices: acceleration methods and accelerated particles. Among them, medical institutions with linear accelerators (linacs) occupy most of the radiation treatment facilities. In this method, electrons are accelerated by a linac and used for treatment, and radiation irradiated to a patient is an electron beam or a braking X-ray. In addition, there are several facilities in Japan that irradiate proton beams and heavy particle beams used for treatment by accelerating particles different from electrons.

(Radiotherapy using linac)
Hereinafter, an outline of radiation therapy using a general linac will be described with reference to FIG. A general medical linac radiation utilization apparatus has a rotatable gantry (hereinafter referred to as a gantry 2) supported by a fixed gantry 1. The gantry 2 rotates the patient around the patient laid on the treatment bed 3 clockwise or counterclockwise by 360 degrees along the gantry rotation trajectory R1, thereby irradiating the patient lesion from any angle. Can do. The gantry 2 is provided with an irradiation head 4 that emits radiation toward its own gantry rotation axis A1. During radiotherapy, accelerated electrons collide with a metal called a target, and the braking X-rays generated there are used as X-rays for radiotherapy. When the target site is irradiated with radiation from different angles, the irradiation center that is always the intersection of irradiation is the isocenter I, which coincides with the rotation center of the gantry. The gantry 2 has a collimator 5 at the tip of the irradiation head 4. The collimator 5 forms a radiation irradiation range according to the shape of the lesion. The collimator 5 is composed of two pairs of metal blocks. Further, the collimator 5 can be made closer to the shape of the lesion tumor by rotating along the collimator rotation trajectory R2 around the collimator rotation axis A2 in the plane perpendicular to the beam axis direction. According to the “External Radiation Therapy Device Maintenance Management Program” edited by the Research Committee of the Radiation Oncology Society of Japan, Isocenter I is a “symmetry irradiation by rotating the gantry and the rotation of the irradiation field limited system. It refers to the center of the smallest sphere created by the field beam axis. Here, in terms of the radiation therapy apparatus, the gantry refers to the gantry 2, and the irradiation field limited system refers to the collimator 5. Therefore, the isocenter I means “the center of the smallest sphere formed by the beam axis of the symmetric field by the rotation of the gantry and the rotation of the collimator in the treatment apparatus in which the gantry rotates”. In the gantry, a substance having a high atomic number such as lead or tungsten is used as a shielding material for the purpose of preventing radiation from leaking in directions other than the beam traveling direction during radiation irradiation. Therefore, since the super-heavy structure has several tons, the burden on the mechanical operation over time is large. Therefore, the position accuracy management of the isocenter I is important in assuring the treatment accuracy.

(Radiotherapy with proton beam and heavy particle beam)
The apparatus used for radiotherapy with proton beams and heavy particle beams has the same configuration of the gantry and irradiation unit as the above-described radiotherapy apparatus. A powerful electromagnet is required to deflect the proton beam or heavy particle beam in the target direction, and the weight of the gantry exceeds 100 tons. The gantry of the proton beam therapy apparatus also has a structure that rotates around the isocenter, and periodic quality control is important in controlling the apparatus in millimeter units.

(Radiotherapy method using radiotherapy equipment)
Using such a radiation therapy apparatus, radiation therapy is usually performed in the following procedure.
(1) In order to determine the optimal irradiation direction and irradiation area, CT imaging for treatment planning is performed, and a radiation treatment plan is made based on the obtained CT image. In the treatment plan, the center of the lesion and the isocenter are matched so that irradiation is performed from a plurality of directions. The surface of the patient's body is marked with a seal or special ink based on the position and size of the lesion obtained in the treatment plan. When radiotherapy is performed on the lesion on the head, it is necessary to prevent positional shifts due to differences in jaw inclination and to improve reproducibility of patient fixation. Therefore, a fixture like a mask is created for each patient to improve the fixing accuracy and reproducibility. Also, when using the fixture, the surface is marked.
(2) Lay the patient on a therapeutic bed. A position confirmation laser indicating the isocenter is installed on the wall or ceiling of the radiation treatment room, and the treatment bed is moved so that the laser is projected onto a marking applied to the body surface of the patient. If the laser does not match the marking only by moving the treatment bed, adjustment is made by shifting the tilt of the patient's body.
(3) The gantry of the radiotherapy apparatus is rotated around the isocenter, and the target site that is the lesion is irradiated with radiation from different angles.
(4) In some cases, the treatment bed is also rotated around the isocenter and irradiated with radiation from various directions.
(5) Radiation treatment is generally performed in several Gy per day, divided into several tens of times. In some cases, the dose to be administered per dose is increased, and one or several irradiations are also performed.

  With the recent remarkable progress in radiotherapy technology, the concentration of the dose to the lesion and the dose reduction to the surrounding normal tissue are improved. For this purpose, advanced irradiation techniques are required, and it is important to accurately irradiate the lesion with a precision of millimeter units or less. In performing radiation therapy, in order to suppress skin damage to the patient, irradiation is performed by dividing from a plurality of directions. By irradiating from multiple directions, the dose to normal tissues such as skin can be dispersed while concentrating the dose at the lesion. Actually, irradiation in only one direction is rare in radiotherapy, and usually multiple portal irradiations in two or more directions are performed. A motion irradiation method in which radiation is irradiated while rotating the gantry may also be performed. Normally, when irradiating from one direction, the device is designed so that the radiation intensity in the irradiation field is uniform, but the intensity in the irradiation field is modulated by a multi-leaf collimator (multi-leaf collimator) or a metal filter, etc. A treatment method that reduces the dose to normal tissues by irradiating from the direction is called intensity modulated radiation therapy (IMRT). Furthermore, IMAT (Intensity Modulated Arc Therapy), which performs IMRT while rotating the gantry, has many advantages over conventional radiotherapy such as shortening of treatment time. Since the apparatus is very heavy and may be worn out or deteriorated with repeated use, it is necessary to periodically verify the operation accuracy of the apparatus. In performing radiotherapy, a radiotherapy planning device is used to calculate the dose to be administered to the lesion. When performing irradiation from a plurality of directions, in the treatment plan, the gantry head section and the target installed therein are registered to rotate along a circular orbit. Here, if the actual rotational trajectory of the device is deviated from the circular trajectory, a difference in the distance from the target to the lesion may occur, and the dose calculation result may differ from the actual dose distribution. Since it is necessary to circularly move a gantry with several tons, a large load is applied to the rotating shaft connecting the fixed mount and the gantry. Therefore, it is necessary to verify the rotation trajectory not only when the apparatus is installed but also periodically.

  Conventionally, as a verification method for confirming the rotation trajectory of a gantry, a star shot analysis method using an X-ray film or an imaging plate, a metal sphere is arranged at an isocenter position, and the deviation between the sphere and the irradiation field is confirmed from each gantry angle. Method, an ultrasonic method using an ultrasonic distance meter, an infrared (IR) -camera method using an infrared sensor for respiratory synchronized irradiation, and the like.

(Star shot method)
A detector such as an X-ray film or an imaging plate is placed on the treatment bed so as to be perpendicular to the gantry rotation axis on the isocenter. A collimator irradiates the beam thinly toward the aperture detector. By irradiating one detector from a plurality of directions by changing the angle of the gantry, a line of a plurality of radiations is drawn. The image acquired by the detector is analyzed, and the center of gravity of the region connected by the line from each angle is obtained, thereby obtaining the isocenter of the beam and the variation of the beam axis (see, for example, Patent Document 1).

(Winston Lutz method)
A metal ball having a diameter of about 2 cm is placed on the treatment bed or the like independently of the gantry at the isocenter position. An auxiliary tool such as a stick is attached from the head part so that the positional relationship is always fixed with respect to the target so that the X-ray film for photographing can be fixed to the tip. A metal sphere is photographed with a film from an irradiation field reduced to several centimeters by a collimator of the irradiation head. The metal ball remains fixed on the treatment bed and is independent of the gantry rotation axis. The gantry angle, collimator angle, and the position of the metal ball are not aligned even when the treatment bed is rotated. By confirming whether there is any, the isocenter coincidence of the gantry, collimator, and treatment bed is confirmed (for example, see Non-Patent Document 1).

(Ultrasonic method)
A metal ball is placed at the tip of the treatment bed and placed at the isocenter position. Attach an ultrasonic rangefinder from the head to the isocenter. While rotating the gantry, measure the distance of the metal sphere installed at the isocenter with an ultrasonic rangefinder to check whether the gantry is drawing a circular orbit. If the metal sphere is accurately placed at the isocenter and the gantry is orbited around the isocenter, the distance indicated by the ultrasonic rangefinder is always constant.

(IR-camera method)
Attach an infrared reflector near the isocenter of the gantry head. By using an infrared sensor for synchronized breathing irradiation, it is verified whether the gantry rotation is a circular orbit by reading the trajectory of the reflector during the gantry rotation. It is possible to similarly verify the rotation trajectory of the collimator and the rotation trajectory of the treatment bed (for example, see Non-Patent Document 2).

(Front pointer method)
Attach a jig called the “front pointer” that points to the attachment-type isocenter to the head of the gantry. In this state, rotate the gantry and visually check whether the front pointer tip matches the external laser beam pointing to the isocenter from the radiation treatment room wall, and verify that there is no distortion at the rotation center of the gantry. To do.

JP 2008-46422 A

Ken R. Winston, and Wendell Lutz. : Linear Accelerator as a Neurological Toll for Stereotactic Radiology Neurology Vol. 22 (3) 1988, 454-464 Yuria Lyatskaya, Dyanesh Kadam, Gennady Levisky, Fred Hacker, and Lee Chin: Evaluation of a new IR for the guided system for mechanical quasic. 35 (11) 2008, 4816-4823

  The above-described rotation operation verification technology has the following problems. In the star shot method, the Winston Lutz method, and the ultrasonic method, the verification accuracy is greatly influenced by the arrangement method of the detector and the metal sphere, so that it takes time to arrange these instruments. Moreover, it takes tens of minutes to several hours to perform a series of operations from verification to analysis. The IR-camera method requires a dedicated jig for each verification method, such as the necessity of an infrared sensor for respiratory synchronized irradiation, and these are expensive products. In the front pointer method, the shift of the rotation center of the gantry can be confirmed without irradiating radiation, but it cannot be objectively evaluated as a numerical value. In addition, these verification methods cannot directly verify the rotation trajectory during the treatment when performing radiation therapy while rotating. Since the accuracy verification items of the radiation therapy device are very diverse besides isocenter verification, it is important to improve work efficiency. Establishment of a method for verifying a rotating trajectory in a short time and with high accuracy is desired in the medical field.

  In order to solve the above-mentioned problems, a first means of the present invention is a rotation operation verification system for a rotating part in a radiotherapy apparatus, which is fixed to the rotating part and detects acceleration or an angular velocity in addition to it at a predetermined interval. Detection means for performing detection, transmission / reception means for detection data by the detection means, and determination means for comparing the detection data with preset target motion data or past detection data to determine distortion of the rotational trajectory. It is characterized by that.

  The second means is the rotational operation verification system according to the first means, characterized in that the rotating part is a gantry, a collimator or a treatment bed.

  The third means is the rotational motion verification system according to the first or second means, wherein the detection means is a triaxial acceleration sensor or a triaxial angular velocity sensor in addition thereto.

  The fourth means is the rotational motion verification system according to any one of the first to third means, characterized in that the target motion data is perfect circular orbit data centered on the rotational axis of the rotating part.

  Further, the fifth means is a method for verifying the rotational motion of the rotating part in the radiotherapy apparatus, the step of detecting an acceleration during the rotational motion of the rotating part or an angular velocity in addition to the acceleration at a predetermined interval, and then the detection. A step of inputting data, and a step of comparing the input data with preset target motion data or data detected in the past to determine the distortion of the rotating trajectory. .

  The sixth means is a program, and causes the computer to execute each step of the rotational motion verification method described in the fifth means.

  The seventh means is a computer-readable recording medium on which the program described in the sixth means is recorded.

  According to the present invention, it is possible to verify the rotational operation of the radiotherapy apparatus in a short time and with high accuracy by analyzing data acquired by an acceleration sensor or the like. In addition, if a dynamic or position detection monitor such as an acceleration sensor or an angular velocity sensor and a wireless or wired data output device are attached to a location that does not affect irradiation, the operation of the radiation therapy device and the patient can be performed even during radiotherapy. Real-time detection and verification immediately after acquisition. Furthermore, by constantly attaching these sensors to the gantry head portion that does not affect the radiotherapy, it is possible to record changes over time in the rotational position of the gantry head. If it is used for checking the rotational trajectory at the start of inspection, the accuracy of a simple radiotherapy device can be verified, and if it is installed in a rotating device such as a gantry for a long time, the state during the period is detected. It is possible to obtain maintenance data of the device configuration. In addition, the existing radiotherapy apparatus is accompanied by a mechanism for outputting the indicated value of the gantry angle, but the indicated value can be calibrated.

It is the figure which showed the axis | shaft regarding the rotational motion of a radiotherapy apparatus. It is a functional block diagram of the rotation operation verification system according to the embodiment of the present invention. It is a figure explaining the whole processing flow of a rotation operation verification system. It is a schematic diagram which shows the example of installation of a sensor, and the flow of a process. It is the figure which analyzed the acquired data and compared the measured value and the theoretical value. It is the figure which analyzed the acquired data and showed the difference of a measured value and a theoretical value.

  Embodiments of the present invention will be described with reference to the drawings. FIG. 2 is a block diagram of the rotational operation verification system in the present embodiment. The rotational motion verification system includes a data detection unit 21 that detects and collects gantry movement, a data transmission / reception unit 22 that transfers acquired data to an analysis device, a determination unit 23 that analyzes the acquired data, and a past acquisition. DB 24 for storing the data and display means 25 for displaying the results.

  The data detection means 21 is a means that is attached to the gantry of the radiotherapy apparatus and can measure acceleration in the XYZ triaxial directions orthogonal to each other or an angular velocity in addition thereto, and an acceleration sensor or an angular velocity sensor is used in addition thereto. . The data transmission / reception means 22 includes a transmitter that transmits data obtained by the data detection means 21 and a receiver that receives the data. The determination unit 23 calculates the rotation trajectory data of the radiotherapy apparatus based on the received data. The display means 25 displays the analysis result. Further, the DB 24 of data acquired in the past is composed of a storage medium such as a hard disk.

  Below, the accuracy management method of the radiotherapy apparatus by the acceleration sensor which is one of the embodiments of the present invention will be described. FIG. 3 is a flowchart showing a processing procedure by the system shown in FIG. FIG. 4 schematically shows the processing procedure. In step S31, the XYZ triaxial acceleration sensor 6 is attached to the gantry head portion. Secure the sensor with a special jig so that the sensor does not move due to vibration during operation. The acceleration sensor 6 needs to continuously store acceleration data with respect to the XYZ three axes. The surface to be affixed should be a flat part such as a metal plate in the head part cover or collimator part that is not directly exposed to radiation. The affixing unit is preferably always installed in a place where radiation treatment is not hindered for the purpose of confirming the reproducibility of the rotation trajectory (step S36), which will be described later. It is also the first condition that it is installed at the same location for each measurement.

  In step S32, the gantry of the radiotherapy apparatus is rotated 360 degrees or more.

  In step S33, acceleration data collection is started by the acceleration sensor. Since the gantry rotation speed requires about 1 minute to rotate 360 °, the measurement interval (sampling frequency) is assumed to be about 10 Hz to 100 Hz, but this frequency bandwidth corresponds to the object to be detected. .

  When rotating the gantry 360 degrees or more, the same operation is repeated along with the rotation direction with the same gantry operation start position (rotation start position). Alternatively, even if the operation is not started from an arbitrary angle, when the gantry head is vertically below or near the top, the point where the absolute value of the acquired acceleration data is close to the gravitational acceleration is used as the starting point for evaluation. It is effective though it is inferior to. The gantry is operated from the controller or console attached to the linac.

  After the gantry has been rotated, acceleration data is transferred to the computer in step S34. The acceleration data measured by the acceleration sensor 6 is transferred along a transfer path 7 by wireless or wire. As a method of transferring acceleration data, a method of transferring using a cable or the like, a method of transferring information stored in a sensor into a memory card and transferring it to a computer, a wireless communication using a sensor having a transmitter capable of transmitting measured acceleration data. Although there are methods, data transfer by wireless communication is most desirable from the viewpoint of operation efficiency.

  Since the acquired acceleration data is obtained simply by pasting the acceleration sensor on the gantry head portion or the like, the acceleration sensor triaxial XYZ also becomes a rotating coordinate system according to the operation of the gantry. Therefore, if the rotational speed of the gantry is constant (constant angular speed), it can be predicted that the biaxial gravity acceleration data value that is horizontal to the gantry rotating surface fluctuates in a sine wave manner. The axis perpendicular to the plane of rotation corresponds to the gantry rotation blur and tilt. From this, it is possible to verify the stability of the rotational speed by comparing the difference of the measured values with the sine wave of the acceleration value assumed in the gantry rotational motion as the reference value when the angular velocity is constant, and The reproducibility of the rotation operation can be confirmed. The receiving device 8 can receive acceleration data transmitted from the transmitter of the acceleration sensor 6.

  In step 35, the transferred acceleration data is analyzed. The analysis software 9 can calculate rotational orbit data of a gantry head or the like based on acceleration data received by the receiving device 8. The computer 10 is equipped with analysis software 9.

  In step 36, the acceleration data transferred to the computer is analyzed. In this embodiment, the trajectory is analyzed based on the assumption that the angular velocity is constant. If the angular velocity is constant, the acceleration of the sensor itself is 0, and acceleration information other than the gantry rotation axis direction component becomes sinusoidal due to the change in the direction of gravity accompanying rotation. The sine waveform when the angular velocity is constant is defined as a theoretical value T. By comparing this with acceleration data (measured value) obtained from an actual gantry operation by the acceleration sensor, the trajectory distortion with respect to the theoretical value T is analyzed. The theoretical value T is obtained from Equation 1.

  Here, t represents the time from the start of sampling, and a, b, c, and d are calculated by the least square method with the measured value. At this time, the measurement value is extracted and used after the start of rotation starts and the acceleration is stable. When the sensor is installed, it is possible to convert acceleration information into gantry angle information by attaching the sensor so that the acceleration is zero when the gantry is positioned in the 180 degree direction with a level meter. Moreover, in order to compare a measured value and a theoretical value, it evaluates using a determination coefficient. The coefficient of determination is obtained by dividing the theoretical sum of squares of deviation by the sum of squares of deviation of measured values. The closer the determination coefficient is to 1, the more theoretically it is rotating. If the coefficient of determination falls below a certain value (for example, 0.99) according to the accuracy required for each facility, perform re-measurement, and if the same tendency is observed, ask the manufacturer of the device for repair. Take action. The difference between the measured value and the theoretical value is also used for the evaluation. The value of the difference is a deviation at the time of gantry rotation with respect to each axial direction. That is, it is better that this difference is close to zero. From the difference graph, it is possible to grasp at which gantry angle the deviation occurs. When the gantry is controlled and rotated, it is a perfect circle, so the roundness of the rotating trajectory can be evaluated from the measured value. In step S39, the verification result is displayed on the computer screen. As a display example, FIG. 5 shows measured values, theoretical values, and verification results of acceleration data for each axis. The vertical axis represents acceleration, and the horizontal axis represents elapsed time from the start of measurement. FIG. 6 shows the difference between the measured value and the theoretical value. In these verification methods, not only the gantry 2 but also the treatment bed 3 and the collimator 5 are rotated to obtain acceleration data, whereby the treatment bed rotation trajectory R3 of the treatment bed 3 and the collimator rotation trajectory R2 of the collimator 5 are obtained. Verify about. Furthermore, it is possible to verify the accuracy of circular orbits by attaching sensors not only to radiotherapy devices but also to radiological diagnostic devices that involve rotational motion, such as gamma cameras and angiography devices. It leads to quality control.

  The sensor attachment position and analysis method are the same as described above, but other embodiments are shown below. The same measurement is performed at different dates and times, the measured values at different dates and times are compared (step S37), and evaluation is performed using a determination coefficient, thereby verifying whether the apparatus has been distorted over time. In the case of confirmation of reproducibility, past acceleration data is specified from the DB 24 of data acquired in the past, and is compared with the acceleration data acquired this time for comparison. In step S39, the determination coefficient, which is the verification result, and the waveform graph used for the comparative evaluation are displayed on the computer screen.

  This example is a method of detecting and evaluating the tilt and the rotation angle when the rotation speed of the gantry changes when acquiring data. A change in the rotational speed of the gantry means that the angular speed changes during measurement. In this case, the above-described evaluation is performed by using the information of the angular velocity sensor and taking into account the change in velocity. For detection of data, a detector in which both a three-axis acceleration sensor and an angular velocity sensor around three axes are bundled is used. By using the angular velocity sensor, it is possible to detect that the (X, Y, Z) coordinate system is rotating as a result of the rotational motion, so it is more accurate without assuming the preconditions (constant angular velocity) as described above. Trajectory evaluation (step S38) is possible. This verification method can monitor and evaluate the gantry rotational motion trajectory not only during rotational motion but also during radiation therapy other than prescribed (constant) motion. Since the acceleration sensor detects gravity, it can grasp the inclination of the sensor with respect to the ground, and can monitor and compare with the gantry rotation angle output from the existing mechanism in the radiotherapy device. It can also be used for a simple check of the gantry rotation trajectory when there is a possibility that the device will be distorted.

DESCRIPTION OF SYMBOLS 1 Fixed base 2 Gantry 3 Treatment bed 4 Irradiation head 5 Collimator 6 Acceleration sensor 7 Transfer path 8 Receiving device 9 Analysis software 10 Computer A1 Gantry rotation axis A2 Collimator rotation axis I Isocenter R1 Gantry rotation path R2 Collimator rotation path R3 Treatment bed Rotating orbit 21 Data detection means 22 Data transmission / reception means 23 Determination means 24 DB
25 Display means

Claims (7)

A rotational motion verification system for a rotational part in a radiotherapy device,
Detection means fixed to the rotating part, and detecting acceleration or angular velocity in addition to the acceleration at a predetermined interval;
Means for transmitting and receiving detection data by the detection means;
A rotation operation verification system comprising: a determination unit that compares the detection data with preset target operation data or past detection data to determine distortion of the rotation trajectory.   The rotation operation verification system according to claim 1, wherein the rotation part is a gantry, a collimator, or a therapeutic bed.   The rotational motion verification system according to claim 1 or 2, wherein the detecting means is a triaxial acceleration sensor or a triaxial angular velocity sensor in addition to the triaxial acceleration sensor.   The rotational motion verification system according to any one of claims 1 to 3, wherein the target motion data is perfect circular orbit data centered on the rotational axis of the rotating part. A method for verifying the rotational motion of a rotating part in a radiotherapy device,
Detecting the acceleration during the rotation operation of the rotating part or the angular velocity in addition thereto at a predetermined interval;
Then inputting the detected data;
Next, the rotational motion verification method comprising: comparing the input data with preset target motion data or data detected in the past to determine distortion of the rotational trajectory.   A program for causing a computer to execute each step of the rotational motion verification method according to claim 5.   A computer-readable recording medium on which the program according to claim 6 is recorded.

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