Benchmarking the model against the MD Anderson Cancer Center scenario

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 [

11]. 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 [

13] and Thomas [

14] 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 . 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.

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.

Sensitivity analysis of the MD Anderson Cancer Center system

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.

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.

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 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. 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 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 (), 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 , 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 . The increase in the throughput capacity () is a consequence of much shorter waiting times per beam (), and this in turn is the result of lower saturation levels within the system () 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.

Simulation of potential UK scenarios

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 [

4]. 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 [

7], 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.

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.

| **Table 2**Summary of simulations of other four-room scenarios |

A simple calculation of the capacity of a facility in terms of the number of patients that can be treated per year (

*P*_{annual}) can be made using Equation (4), where

*N*_{rooms} is the number of treatment rooms in the facility,

*N*_{weeks} is the number of weeks the facility is open per year,

*N*_{days} is the number of treatment days per week,

*N*_{fractions} is the mean number of fractions per treatment course,

*t*_{day} is the length of each treatment day,

*t*_{fraction} 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. 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%.

| **Table 3**Summary of annual throughput predictions for a UK facility for: *N*_{weeks}=51; *N*_{days}=5; *N*_{fractions}=28; *t*_{day}=14 h; and *U*=95%. Results are presented for a US-type caseload (equivalent to Scenario 1 in ) and a UK-type caseload (equivalent to Scenario (more ...) |

As 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 [

7]. 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.