modelling and control of patient support system for...

Modelling and control of patient support system for radiotherapy

R. Spriestersbach*xo, O.C.L. Haas*x, K.J. Burnham* xBiomedical Engineering Systems Group, *Control Theory and Applications Centre,

Coventry University, Coventry, UK, http://www.ctac.mis.coventry.ac.uk/ oElekta Ltd, UK

Keywords: control, medical, modelling, PID, radiotherapy, SimMechanics.

Abstract

This paper describes a SimMechanics model of the computer controlled patient support system. The first part of the paper describes the aim of the Elekta Synergy radiotherapy treatment machine and in particular the new automatic patient support system (PSS). The second section describes the mechanistic model implemented using the SimMechanics toolbox. The third section describes the implementation of a discrete PID controller onto the PSS microcontroller. The control system is used to demonstrate the ability of the model to replicate the PSS behaviour and highlights that the new PSS control system is able to position patients with a very high accuracy.

1 Introduction

Cancer in the UK is amongst the three leading causes of death at all ages except for pre-school age children. The most common killers are lung, breast, colorectal and prostate cancer which together account for about 62,000 deaths each year. In order to tackle this devastating disease the UK government made cancer one of the four main national priorities set out in Saving Lives: Our Healthier Nation (OHN) White Paper published in July 1999 [1]. Cancer can be treated using a variety of techniques; the most widely used treatments involve chemotherapy, surgery, radiotherapy and combinations thereof. This paper focuses on the application of systems modelling and control techniques in the design and development of new, improved devices for treatment machines used in radiotherapy. It builds on work presented in [2, 3] dealing with the exploitation of systems modeling techniques and control to improve the delivery of radiotherapy treatment, and simulate the effect of new treatment modalities. The patient support system (PSS) from the Elekta Synergy™ system [4] is a sophisticated radiotherapy treatment suite where the PSS is used to exploit the information provided by the integrated X-ray Computed Tomography (CT) device to locate the

patient accurately prior to treatment. This work involves the design of a new control system for an existing device. This incremental improvement is an example of evolving technology, for it exploits the knowledge and experience gained with the current electromechanical devices and control systems. The first part of this paper describes the approach adopted to modernize a patient support control system with the aim to retrofit this to existing patient support systems. Following a description of the system, the paper focuses on the modelling of the PSS electromechanical components. A new mechanistic component-based model is implemented using the SimMechanics toolbox [5]. A control scheme based on Proportional, Integral and Derivative (PID) is then described and used both to validate the system model and demonstrate the ability of the PSS to move the patient smoothly and accurately.

2 Patient support system

This section comprises a brief description of the background to the research, followed by a description of the system to be controlled and the modelling of its various components.

2.1 The need for accurate patient positioning

The latest developments in radiotherapy aim to exploit the information from imaging devices to modify the treatment parameters in real time. In some cases, it may be necessary to modify the patient location using the PSS remotely. The work presented in this paper is part of a Knowledge Transfer Partnership project aimed to improve the PSS control system to move the patient consistently in a sufficient response time and accuracy to correct for organ motion. The set point, that is required to be accurately followed, can be calculated from the information received from real time imaging facilities such as kV CT [4] or portal imaging. A significant amount of investment is currently taking place to develop systems capable of combining images used at the planning stage such as CT, magnetic resonance imaging (MRI), or functional imaging such as positron emission tomography (PET), with those used at the

Control 2004, University of Bath, UK, September 2004 ID-023

positioning and delivery stage. The work reported in this paper assumes that it is possible to calculate in real time the set point to accommodate for target displacement during treatment, and focuses on the control system design. Existing systems require the use of external imaging devices to monitor the patient or the positioning of the PSS. The system described in this work relies on the PSS on-board position sensors. Such a system is more robust and less expensive to manufacture and maintain than imaging based feedback systems. It requires, however, accurate positioning data from the sensors used.

3 The patient support system

The first stage in the controller design was to understand the system to be controlled and to model relevant components. The PSS is used to move the patient vertically (Z-axis), right and left (Y axis), forward and backward (X-axis) and finally rotate it about the isocentre (I axis), see Figure 1. Because it is used in a medical environment where it interacts with people, it is necessary to limit the forces within the system. This means that relatively low power motors, compared to manufacturing and assembly robots, are used to move the various parts of the PSS. As a consequence, friction in bearings, position and mass of the load and the meshing of gears have a greater impact on the control system than for industrial robots with powerful drives. In addition, the table supporting the patient is subject to deflection, the amount of which changes with the patients’ mass, size and position. This variable deflection can also affect the linearity of the system. To develop a practical control system it is important to analyse the performances of the current system. Indeed, depending on the components specification, limiting degrees of accuracy, in terms of accuracy of the controlled system, are achievable. In this work, particular attention was given to position sensors, actuators, and load variations.

3.1 The position sensors

Potentiometers and encoders have been investigated to measure the PSS displacement along the longitudinal, the latitudinal, the vertical and the rotational axes denoted X, Y, Z and I, respectively, see Figure 1. To ensure accurate control, it is necessary to use encoders with a greater resolution than that required to achieve the overall controlled system specification in terms of accuracy and reproducibility. Initially the potentiometers used exhibited some nonlinearities. These nonlinearities were analysed

using a representative number of potentiometers. A linearisable range was then identified and a common pattern was then extracted and used to produce a function to compensate for the sensor nonlinearity. Linearisation of the potentiometers improved the sensor accuracy by a factor of two, leading to a reduced error of the order of a fraction of a millimeter. This was sufficient to allow preliminary parametric modelling. The accuracy of the measurement system was further improved using a new potentiometer arrangement. The latter was shown to be at least as accurate as an independent three dimensional tracking system, namely the NDI PolarisTM device [6]. Potentiometers are analogue devices, therefore, it becomes necessary to convert their reading to digital. This conversion adds an additional source of error. Such error can be kept to a minimum using high resolution analogue to digital converters. Alternatives to potentiometers are digital encoders. Such encoders were investigated and were found to work well, however, radiation testing highlighted a number of key issues that had to be resolved by the encoder manufacturers before they could safely be used.

3.2 The actuators

The actuators are motors used to move the PSS about the X, Y, Z and I axes. The motors were selected to provide sufficient torque to move the PSS and patient. To minimise the controller complexity the motors used have special windings designed to prevent motor cogging. The X, Y and I axes make use of a Maxon RE max 29 with metal brushes, whilst the Z drive uses a custom built motor.

3.3 Known disturbances affecting the system

Depending on the type of treatment, patients are currently positioned and immobilised with various devices to ensure that the radiation delivered conforms to the intended target. The mass and position of the patient as well as the mass of the immobilisation devices will influence the load distribution on the PSS. Such load distribution will affect the mechanical components of the PSS structure. The structure is designed to be as rigid as possible, however to facilitate radiotherapy treatment, some sections of the PSS are designed so as not to inhibit the passage of radiation. In [7] it was shown that the design of the Elekta C-arm PSS allows greater treatment flexibility. Indeed, it is possible to move the C-arm to allow radiation exposure from a wide range of gantry angles to strike the target without being attenuated by the C-arm mechanical frame. The drawback is that the C-arm reduces the rigidity of the PSS and causes a small displacement to occur for particular PSS positions. Such deflection has to be taken into account if very


accurate patient positioning is to be achieved. To compensate such flexion and minimise the interactions with radiotherapy beams, so called ‘table tops’ such as the C-arm are constantly being redesigned. The model as well as the new control system should be able to adapt to such design change.

4 Modelling of the PSS

In [3] it was shown that X-axis of the PSS could be modelled effectively using both parametric and mechanistic models based on first principles. A second order Auto Regressive Moving Average with eXogeneous inputs (ARMAX) model with a position dependent gain was found to model the system adequately [3]. The structure of the ARMAX model was chosen such that it replicated a simplified model of the system that could be used to design and tune a controller. The second approach was to develop a model based on the physical properties of the mechanical components of the PSS. The model was developed using the SimMechanicsTM toolbox [5]. The two modelling approaches were compared and it was found that the SimMechanicsTM model led to models that are easy to understand and relate to the actual system components. Each mechanical component, including nonlinearities, can also be modelled independently and then combined. For example, if an aspect of a system component changes, such as its mass, it is only necessary to update that aspect of the component. It was also found that making use of such an approach could help verify the mechanical system specification and implementation. It was therefore decided to develop a SymMechanicsTM model for all the axes of the PSS. This model is described in the remainder of this section.

4.1 Mechanistic modelling

A number of packages exist to model mechanical structures. In this work the SimMechanics Simulink toolbox was used. SimMechanics defines a set of basic mechanical elements, such as joints, gears and rigid structures. These elements can be combined together to form complex systems. The following approach has been used to create a mechanical representation of the PSS. The shape, mass and centre of gravity of the rigid bodies were defined using information from computer aided design drawings. The rigid bodies were then linked together using joints, dampers and gears. Finally, actuators and sensors were included to provide an interface with other Simulink blocks and toolboxes. The mechanical system is represented by a set of masses that simulate the inertia of the mechanical system components. These blocks are connected together using a

combination of bearings and function blocks such as springs and dampers. The mechanical system is then interfaced using a combination of function blocks that simulate the behaviour of the drive system. This system recreates the characteristics of the motor–gearbox combination and is able to translate a given input voltage into the related force or torque that is applied to the moving parts of the system. To facilitate an understanding of the model by other engineers in the team a modular approach was adopted. Each axis is modelled independently and then combined with the other axes using so called ‘weld’ SimMechanics blocks. The mechanical components include the effect of stiction, friction and nonlinearities affecting the system. The sensors are modelled to take into account their accuracy. Similarly the effects of analogue to digital converters are included as well as effects of sampling and overall system clock. An example of a SimMechanicsTM model is represented in Figure 2. The implementation of the whole PSS is relatively complex and requires a large amount of information regarding the different PSS components. The use of variables from actual component datasheets allows a check that the system has been manufactured according to specification. It also helped in the study of alternative components e.g. sensors or actuators to improve the overall system accuracy and performances. If a new component is adopted, then it is only necessary to change the parameters of a few blocks according to manufacturers’ datasheet. In addition if the load characteristic changes, it is only necessary to change the variables corresponding to the mass and the centre of gravity position of a particular rigid body. This can also be used to study the effect of patients’ weight distribution on the control system performances.

5 The PSS controller design

5.1 Controller specification

The first aim of the PSS control system is to enable the PSS to position the patient, and, in particular, the planning target volume (PTV), within 1.0 mm in terms of absolute error. In addition, the PSS control system should be sufficiently responsive to track organ movements during treatments accurately and repetitively. This means that the PSS should be able to compensate for the patients breathing cycle, which is one of the main sources of organ motion. The PSS drive system has been designed to generate speed and acceleration levels, which are more than sufficient to relocate the patient’s PTV. The application is safety critical and warrants the use of


safe and robust control systems. Proportional Integral and Derivative (PID) controllers are the most widely used and accepted in industry requiring good performances as well as safe and robust design. It was therefore decided that the first control system to be implemented would be a standard discrete PID controller incorporating limiters for proportional, integral and derivative control actions.

5.2 Movement profile calculation

The aim of the control system is to move the patient comfortably. A smooth desired movement profile (i.e. the set point) is calculated. It uses information such as maximum allowed speed, current speed, maximum allowed acceleration, deceleration actuator output percentage and current position. This information is used to estimate a new set point for each iteration to ensure that the patient is subjected to a conservative acceleration rate and displacement speed. The profile calculation modifies the initial set point demand, which is in terms of final desired position.

5.3 PID controller

The aim of the controller is to reach the required position with a maximum error of 0.2mm and the PSS movement should be sufficiently smooth to ensure minimum achievable patient discomfort. For large movements a proportional controller is used. For small displacements a PID controller has been implemented with limits on the contributions from the proportional, the integral and the derivative control actions. To reduce the effect of noise some filtering and averaging was also implemented. The controller was first written in Matlab, then Simulink and finally ported to C++ where it was implemented onto a microprocessor. The PID was tuned to achieve two different purposes: first, to demonstrate the ability of the SimMechanics model to replicate the behaviour of the closed loop system and second to provide a fast response with no overshoot.

6 Experimental verification of PSS model

To assess the model developed, the X, Y and Z-axes of the PSS were subjected to movement requests within the working envelope of the system. For example, the PSS was moved along the X-axis from -300mm to +100mm. The PSS trajectory along the X-axis was calculated using the movement profile generator to ensure smooth displacement. Figure 3 shows a comparison between the measured displacement and the simulated displacement of an unloaded PSS for a system subject to a 400 mm step change. It can be observed that the PSS is able to follow the pre-calculated trajectory with a final error well within the required resolution of 0.1mm.

7 Conclusions

This paper has described the application of a systems modelling and control approach in medical technology and in particular radiotherapy. A new compartment-based mechanistic model of a patient support system has been developed using SimMechanics and Simulink. The model was validated and used to design the current PID control system. The PSS control system has been evaluated experimentally and was shown to be able to achieve the required resolution of 0.1mm. Using mechanistic modelling, it is possible to compare each of the actual system components with a validated model representation. The model developed was used to study the system, verify the mechanical and electrical system design and determine applicable control strategies. The systematic approach adopted during the modelling stage has helped to identify a number of issues with the actual hardware. In particular, by corroborating the experimental measurements with the simulation results it has been possible to improve the setting up and tuning of some of the hardware and software components.

Acknowledgements

The work presented in this paper is supported by the TCS Grant No 3787.

References

[1] Great Britain Department of Health, Saving Lives: Our Healthier Nation 6th July 1999 xiv, 159p. ISBN: 0101438621, (1999)

[2] O.C.L. Haas, “An Intelligent Oncology Workstation for the 21st Century”, Nowotwory Journal of oncology, 53(4), 389-397 (2003).

[3] R. Spriestersbach, O.C.L. Haas, K.J. Burnham, J. Allen, “Modelling of a patient positioning system: A precursor to control systems design”, Proc 16th Int Conf. On Systems Engineering, ICSE2003, Coventry University, Coventry, UK, 9-11 Sept 2003, (2):852-855, (2003).

[4] Elekta Synergy™, 3-D Image-Guided Radiation Therapy System, .http://www.elekta.com/ ContentInternational.nsf (accessed 16/07/2004).

[5] Matlab, The MathWorks (accessed 3-2-2004) available from http://www.mathworks.com/

[6] NDI Polaris, http://www.ndigital.com, (accessed 15/07/04).

[7] J. Meyer, J.A. Mills, O.C.L. Haas, K.J. Burnham, E.M. Parvin, “Accommodation of Couch Constraints for Coplanar Intensity Modulated Radiation Therapy”, Radiotherapy and Oncology; 61:23-32, (2001).


Figure 1: Illustrating the PSS mechanical design (Courtesy of Elekta Ltd)

Figure 3: Illustrating the ability of the X-axis servo control to reach the desired position with the required accuracy. Note that the actual system was sampled at 0.02s, with the sampling of 0.4 being used for illustration purpose.

Zero-OrderHold

Drive input X position

Base Top

X - Drive unit

B F

Weld3

B F

Weld1

CS1

Table top X axis1

Step

-0Start Position

SaturationPulse

Generator

Zero position

Clock

PSS reset

In1 Out1

PSS profilegenerator

E U

PID controller

Ground

Clock

Figure 2: Illustrating the SimMechanicsTM implementation of the X and the Y-drive model, the X and Y-axis profile generators and the X and Y-axis controller. The ‘Weld’ are blocks that link mechanical sub-systems together.

Input/output to allow mechanical connection with other part of the PSS.

Drive signal for the motor coming from the control system.

X-axis SimMechanics model

X-axis movement profile calculation from required set point

X-axis controller

Position of the X- axis

X-axis initialisation


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