|Home | About | Journals | Submit | Contact Us | Français|
We describe a model for evaluating the throughput capacity of a single-accelerator multitreatment room proton therapy centre with the aims of (1) providing quantitative estimates of the throughput and waiting times and (2) providing insight into the sensitivity of the system to various physical parameters.
A Monte Carlo approach was used to compute various statistics about the modelled centre, including the throughput capacity, fraction times for different groups of patients and beam waiting times. A method of quantifying the saturation level is also demonstrated.
Benchmarking against the MD Anderson Cancer Center showed good agreement between the modelled (140±4 fractions per day) and reported (133±35 fractions per day) throughputs. A sensitivity analysis of that system studied the impact of beam switch time, the number of treatment rooms, patient set-up times and the potential benefit of having a second accelerator. Finally, scenarios relevant to a potential UK facility were studied, finding that a centre with the same four-room, single-accelerator configuration as the MD Anderson Cancer Center but handling a more complex UK-type caseload would have a throughput reduced by approximately 19%, but still be capable of treating in excess of 100 fractions per 16-h treatment day.
The model provides a useful tool to aid in understanding the operating dynamics of a proton therapy facility, and for investigating potential scenarios for prospective centres.
The model helps to identify which technical specifications should be targeted for future improvements.
Radiotherapy using charged particles can have advantages over photon radiotherapy techniques for certain disease sites  primarily because of the reduced collateral dose to normal tissue. At present, Clatterbridge is the only proton therapy facility in the UK, although its maximum proton energy of 60 MeV means that it is limited to treatments of ocular tumours . In 2007 the National Radiotherapy Advisory Group (NRAG)  advised the setting up of a referral system for treatment abroad of UK patients who would benefit from proton therapy for other disease sites, and this system  has been in place since 2008.
NRAG also recommended the formulation of a business case for development of proton therapy facilities within the UK . As part of that work a good estimate of the throughput capacity is critical, both for cost implications  and for the ability to meet the clinical demand, especially for prospective centres in the UK where it is likely that demand will increase substantially over the next few years . One of the options for development of proton therapy facilities in the UK suggested by Jones et al  was the construction of 3 or 4 centres capable of treating ≥1000 patients per year, and ensuring that planned centres are capable of meeting this demand is key to the development of proton facilities in the UK.
Throughput estimates for a proton therapy centre cannot be based directly on estimates for a similarly sized photon centre, since the operation of proton and photon facilities are fundamentally different: because of the cost and size of proton therapy accelerators a number of clinical rooms are generally run from one accelerator (Figure 1), whereas for photon therapy each treatment room typically has a dedicated linear accelerator. Sharing a common accelerator impacts on the operation of a proton therapy facility since the proton beam can only be delivered to a single room at any one time, with other treatment rooms having to wait until it becomes available. The set-up and treatment within each room is a series of complex tasks of varying length, with the result that there is considerable diversity in the length of time an individual treatment may require. Thus, it is not possible to schedule patients to ensure that the beam is always available when needed, and a patient having to wait for the beam is a common occurrence. Compounding this, with current technology the process of switching the beam from one room to another may take in the region of a few minutes, further extending the delay for any room in waiting and impacting on the throughput of the centre. In addition to throughput considerations, minimising the time spent waiting for the beam is important for the comfort of the patient and to reduce the likelihood of movement between set-up and beam delivery.
These limitations of the existing technology are already recognised by manufacturers, and current work on beam splitting and rapid switching technologies should mitigate many of the operational difficulties over time. However, a detailed understanding of the dynamics of single-accelerator, multitreatment room facilities will benefit existing facilities as well as those planned for installation in the near future. These dynamics are complex, and it is difficult to estimate the number of patients such a facility is capable of treating. We have therefore developed a model to reproduce the behaviour of a single-beam, multiroom proton therapy centre. The aims for the model were to provide: (1) quantitative estimates of the throughput and waiting times and (2) insight into the sensitivity of the system to various physical parameters, such as the beam switch time and the patient caseload. Improving the understanding of the system will aid the design of new proton therapy facilities, while also helping to identify which technical specifications should be targeted for future improvements.
The model has been developed to run in a MATLAB (The MathWorks Inc., Natick, MA) or GNU Octave  environment, and employs a Monte Carlo approach, simulating the behaviour of the system over a number of independent days. Throughout each simulated day, each treatment room follows the process flow outlined in Figure 2. The durations of Stages 2, 3, 6, 7, 9 and 10 in the flowchart are defined by the model's inputs, whereas the duration of Stage 5 is dependent on the beam queue at the time the beam is requested, and hence on the status of all the other rooms in the system.
In the first stage of the process the selection of the patient to be treated is made from a pre-defined caseload of patients. The caseload consists of distinct sets of patients grouped according to the indication, such as craniospinal, gastrointestinal and genitourinary. The caseload defines the proportion of patients belonging to each group, and patients are selected at random from the caseload accordingly. The number of fields to be delivered per patient and the patient set-up requirements (Stages 2 and 9) are also defined within the caseload. When modelling an existing facility, the modelled caseload would be configured to match the actual caseload of patients, while for simulations of a prospective UK centre the modelled caseload must be configured to match the indications that it is anticipated will be treated by proton therapy.
The time required for equipment set-up (Stage 3) is dependent on the configuration of the treatment room in question, since this will depend on whether the beam is delivered by a gantry or a fixed beam-line, and on whether scattering or scanning techniques are used. In general, scanning techniques may require less time for equipment set-up, and can have a clinical advantage owing to a reduced dose from scattered neutrons . On the other hand, scanning techniques can be more demanding technologically, and can be more sensitive to patient motion . At present, the majority of proton therapy treatments worldwide are delivered using scattering techniques, although most manufacturers now offer a scanning solution and the prevalence of this technology is likely to increase with time.
A room enters the beam queue (Stage 5) when the equipment set-up has been completed and the beam is allocated to some other room. In a multiroom centre there will often be times when more than one room is waiting for the beam, and queuing rules are required to decide which room is to receive the beam next. Within the model each patient group is allocated a priority level, such that the beam would switch to a room holding a high-priority patient (such as those under general anaesthesia) ahead of other rooms holding lower-priority patients. For patients of equal priority, rooms are queued according to the length of time each room has been waiting. It should be noted that the model always allows the beam to switch rooms after delivery of a field, even if subsequent fields are required for the patient. In that situation, the room would queue to regain access to the beam when ready to deliver the next field.
At beam delivery (Stage 7), the duration is dependent on the treatment site and on whether the room uses scattering or scanning technology. On completion of beam delivery, if no further fields are required then time is allocated for the patient to leave the room.
The model allows random variation to be built into the duration of each stage by adding noise generated on a Rayleigh distribution. The one-sided nature of a Rayleigh distribution makes it more suitable for this purpose than a gaussian distribution, because the stage durations must take a positive value. Figure 3 illustrates how a Rayleigh distribution (having a minimum value which is offset from zero) is used to generate randomly varying process times while also enforcing an absolute minimum on the generated values.
The model makes the following assumptions:
The assumption that patients are randomly selected from the caseload is likely to result in a small reduction in the modelled throughput compared with that which would be achieved if patients were grouped to minimise the need for equipment changes (such as nozzle or couch top changes). However, all the other assumptions tend to lead to the computed throughput being higher than that which could be achieved in a real facility, with the combined consequence that the model is effectively computing the maximum capacity of the system. We expect that the absence of a schedule of appointment times is likely to have the largest impact of these assumptions, and an initial investigation into the impact of patient scheduling has indicated that it may reduce the usable capacity by up to 10–12%. However, further work is required to study this in detail.
The model records the status of each treatment room throughout all simulated days and various statistics are collated from the resulting data, describing the number of fractions delivered, the treatment time for each indication and the time spent waiting for access to the beam. There are several possible measures that could be used to describe the distribution of waiting times, and within this study we have focused on the mean waiting time per beam, since this is the most relevant parameter from a throughput perspective. Other measures may be more suitable from a clinical viewpoint, such as the proportion of patients who are required to wait longer than a given length of time at any particular stage in the treatment process. However, identifying a single clinical measure which is appropriate for all indications is difficult.
In addition to computing the throughput capacity and waiting times for a given facility, the model computes the saturation level of the system as a measure of the system's efficiency. The saturation level can be quantified by considering the duty cycle, D, of the beam using Equation (1), where Nbeams is the total number of beams delivered in one treatment day of length tday and ton is the mean beam delivery time:
In a multiroom centre running at full capacity, it can be assumed that, as soon as beam delivery is completed in one treatment room, the beam can immediately begin switching to the next room in the beam queue. The duty cycle thus has an upper limit, Dmax, which can be computed using Equation (2), where tswitch is the mean beam switch time. It should be noted that in this analysis it is assumed that the set-up time between fields for each patient is longer than tswitch, which is likely to be true for current technology for which nozzle or couch movements generally require treatment staff to enter the treatment room:
The saturation level of the system, given by ratio of D and Dmax [Equation (3)], is a measure of how close the system is to a state in which the beam is in constant use (either in delivery or switching), and is therefore a measure of how efficiently the system makes use of its accelerator:
While a high saturation level in any system implies that the beam will rarely have moments when it lies idle, in practice it is desirable to have a degree of slack in the system since saturation levels close to 100% will lead to long waiting times for access to the beam.
The University of Texas MD Anderson Cancer Center proton therapy facility began treating patients in 2006, and as of August 2010 had treated approximately 2200 patients . The facility is served by a 250-MeV proton synchrotron, and has four treatment rooms as summarised in Table 1. The system is described in detail by Smith et al , and detailed information on the patient caseload, process times and typical throughput volumes are described in the recent report by Suzuki et al .
The data from these reports provide an ideal baseline of a high-throughput clinical facility against which the model can be tested. In configuring the model to perform this test, the following settings and assumptions were made.
The modelled maximum throughput of the MD Anderson facility was 140±4 patients for a 16-h treatment day, in good agreement with the actual utilisation of 133±35 patients . That the modelled throughput was higher than reality was to be expected given the assumptions made by the model: in particular that the system is not limited by a schedule, and that system downtime was neglected.
While the variation in the actual throughput at the MD Anderson Cancer Center is much greater than the model, it is likely that this includes variation in the number of referrals, which was not considered in the model. By comparison, studies of linear accelerator facilities by Thomas et al  and Thomas  have shown that the utilisation of the system should be 5–15% less than the maximum capacity, otherwise random fluctuations in the referral rate will result in unacceptable delays to some patients when the referral rate hits a temporary peak. It is likely that the usable capacity of a proton therapy facility will be less than the maximum capacity by a similar amount, and this should be kept in mind given that the following discussion considers only the maximum capacity.
There was good agreement between the modelled and reported fraction times, as shown in Figure 4. Although the model predicts a slightly shorter treatment time for patients receiving five fields per session, the prediction is within one standard deviation of the actual process time. The variation seen in real life for four and five fields per session is also somewhat greater than predicted by the model, suggesting that the model has not fully captured the variation in process times for complex, many-field treatments. In particular, five-field cases at the MD Anderson Cancer Center are predominantly craniospinal cases involving image guidance for each isocentre, and the variation in the time required for imaging may be underestimated by the model. Nevertheless, treatments of four and five fields per session together make up only 7% of the MD Anderson Cancer Center's caseload, making their overall impact on the system small.
Figure 5 shows the modelled waiting times per beam, in which the waiting time is defined as the time from the moment the beam is requested until it begins the switching process. The impact of beam prioritisation can clearly be seen, as the waiting time for the “CNS_anaes” group (anaesthetised paediatric craniospinal patients) was shorter than for the other groups since it had a higher priority in the beam queue.
Overall, the behaviour of the modelled and physical systems were in good agreement, giving confidence that the model can also be used as a predictive tool to look at the impact of changing the system inputs.
One of the primary aims in the development of the model was to enable the sensitivity of the system to real physical parameters to be studied. Simulations were therefore performed to look at the impact of the following inputs, using the MD Anderson Cancer Center model configuration as the baseline: (1) the number of treatment rooms; (2) the time required to switch the beam between rooms; (3) the patient set-up time; (5) having a second accelerator within the system.
Figure 6a,b shows how the capacity and the waiting times of the system changed as the number of treatment rooms and the beam switch time were varied. As would be expected, adding extra treatment rooms increased the throughput capacity of the system, but at the expense of a longer mean waiting time per beam owing to increased competition for the beam. The greater the number of rooms in the system the more sensitive the system is to the beam switch time, and long switching times may lead to saturation of the throughput and unfeasibly long waiting times in centres with many rooms. Conversely, there may be significant benefits in reducing the beam switch time in existing centres. For example, in the MD Anderson Cancer Center system if it were possible to reduce the beam switch time by 50% then a fifth treatment room could potentially be served by the system, increasing the total throughput capacity by 30% without resulting in any increase in the mean waiting time per beam.
Figure 6c shows that the saturation level of the system increases with both the number of treatment rooms and the beam switch time. For the standard four-room MD Anderson Cancer Center configuration, the saturation level of the system was computed to be 65%, meaning that the beam lies unused 35% of the time. While adding further treatment rooms would make greater use of the available beam-time the saturation level of the system would also increase, and Figure 6d shows that the saturation level is closely linked with the mean waiting time per beam. Higher saturation levels (resulting from the addition of further treatment rooms) would therefore inevitably lead to an increase in the time spent waiting for the beam. As a rule of thumb, the model indicates that saturation levels greater than approximately 75% correspond to mean waiting times of more than 1 min per beam (measured from the moment the beam is requested until it begins the switching process).
Reducing the time required to perform the initial patient set-up in the treatment room by using remote patient-positioning procedures has been reported as a means of increasing throughput [15,16]. To test the potential impact of reducing the patient set-up times within the MD Anderson Cancer Center system, scenarios where all patient-related set-up times were reduced by 50% and 75% were simulated. This test therefore goes beyond what can be achieved using out-of-room set-up, since that can only reduce the set-up times prior to delivery of the first field. Figure 7a illustrates the impact of reduced patient set-up times, showing 17% and 31% increases in throughput for 50% and 75% reductions in set-up times, respectively, for the four-room scenario. The increase in throughput is therefore dependent on the amount by which the set-up times are reduced, as well as on the overall configuration of the centre. Results shown in Figure 7b illustrate an undesirable side effect of reduced patient set-up times—that the mean waiting time per beam increased as the set-up times were reduced. The increase in the waiting times is a consequence of an increase in the saturation level of the system (Figure 7c,d), and therefore of increased competition for the beam. The simulations suggest that in practice, for systems in which the saturation level is already 75% or more, reducing set-up times is not a feasible means of increasing throughput owing to the inevitable side effect of increased waiting times.
Manufacturers of proton therapy facilities have recently been offering systems where the number of treatment rooms served by each accelerator is reduced, opening up the option of multiple accelerators within a single facility. With current technology a two-accelerator system would most likely have two independent sets of treatment rooms, as shown in Figure 8, without sharing a common beam-line.
Simulations were performed to compare a single-accelerator against a double-accelerator system using the MD Anderson Cancer Center's process times and patient caseload. While the cost of building such a system would probably be somewhat greater than for a single-accelerator system, simulations demonstrate that there would be a benefit in terms of throughput, and that the benefit is greater as the number of rooms in the centre increases, as shown in Figure 9. The increase in the throughput capacity (Figure 9a) is a consequence of much shorter waiting times per beam (Figure 9b), and this in turn is the result of lower saturation levels within the system (Figure 9c) resulting in decreased competition for the beam.
Other potential benefits exist for a two-accelerator solution that are not considered by the current model. First, the system will be more tolerant of downtime: if one accelerator were to go offline, then it may be possible to transfer patients and continue treatment in a room served by the other accelerator. In addition to minimising interruptions to a patient's treatment course, the workload for treatment planning could potentially be reduced by eliminating the need for back-up photon plans for every patient. Also, improved access to the beam would be a major benefit for initial commissioning work.
Further simulations were performed to study specific scenarios of interest for a potential UK proton therapy facility, looking at the impact of shorter and longer beam switch times, longer beam delivery times and a more complex patient caseload.
Investigation of different beam switch times is important since other manufacturers may have systems that are faster or slower than that in operation at the MD Anderson Cancer Center, and investigation of longer beam delivery times takes into account the possibility of an increase in the usage of scanned delivery techniques over the next few years. Evaluation of a more complex caseload reflects the different caseload of patients that we anticipate would be targeted for a UK facility, since the current UK list of approved diagnoses for referral abroad consists of a mixture of complex sites . By contrast, a typical US caseload contains a large proportion of less complex genitourinary (prostate) patients: 44% in the case of the MD Anderson Cancer Center. To reflect this within the present study, a UK-type caseload was created by taking the MD Anderson Cancer Center caseload, removing all genitourinary patients and replacing them with additional craniospinal patients. This had the effect of increasing the mean number of fields per fraction to 2.6, compared with a mean of 2.3 fields per fraction for the standard MD Anderson Cancer Center caseload.
While hypofractionated treatment schemes could potentially increase annual patient throughput [17,18], we limited the study to a consideration of schemes of 28–30 fractions per course, similar to what is likely in a prospective UK centre. For a centre to be capable of meeting the capacity of 1000 patients per year suggested by Jones et al , the daily throughput must be in the region of 105–115 fractions, assuming that 28–30 fractions are typically delivered per course and that the centre is operational 5 days per week, using 16-h treatment days.
Table 2 illustrates the results of the simulations investigating the impact of changing the beam switch times, beam delivery times and the complexity of the caseload. The impact of longer beam switch times and beam delivery times would be relatively small, resulting in a 13% reduction in throughput for an increase in both the switch and delivery times by 50%. Longer switch and delivery times also result in longer waiting times per beam, in the worst case resulting in a mean waiting time of 1.6 min for every beam, a substantial amount of time given that the centre would switch the beam >200 times per 16-h day. In the case where the only change from the standard MD Anderson Cancer Center scenario is a more complex patient caseload, the throughput of the centre would be reduced by approximately 19% to 114±3 fractions per 16-h day, and there would be no change in the waiting times per beam.
A simple calculation of the capacity of a facility in terms of the number of patients that can be treated per year (Pannual) can be made using Equation (4), where Nrooms is the number of treatment rooms in the facility, Nweeks is the number of weeks the facility is open per year, Ndays is the number of treatment days per week, Nfractions is the mean number of fractions per treatment course, tday is the length of each treatment day, tfraction is the mean fraction time and U is the equipment uptime:
Using this equation and the fraction times predicted by the model, the potential annual throughput of a UK facility can be estimated. Table 3 compares the modelled annual throughputs for centres treating US-type and UK-type caseloads and operating 5 days per week with a shorter 14-h treatment day and 95% system uptime (i.e. U=0.95). Results show that the more complex UK caseload has no impact on the mean waiting time per beam, but that the mean fraction time is increased by ~6.5 min with the result that the capacity is reduced by 19%.
As Table 3 shows, a straightforward clone of the MD Anderson Cancer Center 's 4-room facility would be capable of treating ~850 patients per year using a UK caseload and a 5-day treatment week of 14-h treatment days, falling short of the 1000 patients per year suggested by Jones et al . There are a number of possible routes that could be taken to increase this capacity and to ensure that a UK centre is capable of meeting that target: by using a five-room centre rather than a four-room centre at a cost of an increased mean waiting time per beam; by using a double-accelerator system to increase throughput and reduce waiting times; by using a longer working week through either 16-h days or six treatment days per week; by reducing patient set-up times at the possible cost of increased waiting times per beam; by technological improvements such as shorter beam switch times or beam delivery times; by maintaining the uptime of the facility to >95%; or by ensuring that treatment plans use a minimal number of fields to provide an acceptable plan, effectively keeping the caseload as simple as possible. In reality a combination of these approaches is likely to be the best way to ensure that throughput meets the required target.
We have demonstrated the use of a model which simulates the daily operation of a proton therapy centre where multiple treatment rooms share a common proton accelerator. Benchmarking of the model against data for the MD Anderson Cancer Center showed good agreement between the modelled and actual throughput, with the model predicting 140±4 patients per 16-h day in comparison with the actual throughput of 133±35 patients per day. The model also predicts fraction times and beam waiting times that correspond well with those seen in the facility. The good agreement between the model and the data from the clinical centre increases confidence in its use as a predictive tool.
An analysis of the sensitivity of the system to various factors showed that as the number of treatment rooms in a centre increases the system becomes more sensitive to the beam switch time, with long switching times potentially leading to saturation of the throughput and unfeasibly long waiting times. Reducing patient set-up times can increase throughput, but at the same time can lengthen the typical waiting times for the beam owing to increased competition for the beam, especially for systems where the saturation level exceeds 75%.
Several scenarios relevant to a potential UK facility were simulated, with results showing that a centre with an identical four-room, single-accelerator configuration to that of the MD Anderson Cancer Center but with a more complex patient caseload would have a throughput approximately 19% lower than the MD Anderson Cancer Center, but that such a centre would have a maximum capacity of 850 patients per year using a 14-h treatment day and a 5-day treatment week. Various possible routes of increasing the throughput of such a centre to beyond 1000 patients per year have also been highlighted.
To obtain a copy of the software, please contact the authors.
We are grateful to Richard Amos and Kazumichi Suzuki of the MD Anderson Cancer Center for providing data for comparison with the model and for helpful comments on the manuscript.