An Update to the Malthus Model for Radiotherapy Utilisation in England.

AIMS: The Malthus Programme predicts national and local radiotherapy demand by combining cancer incidence data with decision trees detailing the indications, and appropriate dose fractionation, for radiotherapy. Since the last model update in 2017, technological advancements and the COVID-19 pandemic have led to increasing hypofractionation of radiotherapy schedules. Indications for radiotherapy have also evolved, particularly in the context of oligometastatic disease. Here we present a brief update on the model for 2021. We have updated the decision trees for breast, prostate, lung and head and neck cancers, and incorporated recent cancer incidence data into our model, generating a current estimate of fraction demand for these four cancer sites across England. MATERIALS AND METHODS: The decision tree update was based on evidence from practice-changing randomised controlled trials, published guidelines, audit data and expert opinion. Site- and stage-specific incidence data were taken from the National Disease Registration Service. We used the updated model to estimate the proportion of patients who would receive radiotherapy (appropriate rate of radiotherapy) and the fraction demand per million population at a national and Clinical Commissioning Group level in 2021. RESULTS: The total predicted fraction demand has decreased by 11.4% across all four cancer sites in our new model, compared with the 2017 version. This reduction can be explained primarily by greater use of hypofractionated treatments (including stereotactic ablative radiotherapy) and a shift towards earlier stage presentation. The only large change in appropriate rate of radiotherapy was an absolute decrease of 3% for lung cancer. CONCLUSIONS: Compared with our previous model, the current version predicts a reduction in fraction demand across England. This is driven principally by hypofractionation of radiotherapy regimens, using technology that requires increasingly complex planning. Treatment complexity and local service factors need to be taken into account when translating fraction burden into linear accelerator demand or throughput.

Variations in Demand across England for the Magnetic Resonance-Linac Technology, Simulated Utilising Local-level Demographic and Cancer Data in the Malthus Project.

AIMS: Cancer incidence varies across England, which affects the local-level demand for treatments. The magnetic resonance-linac (MR-linac) is a new radiotherapy technology that combines imaging and treatment. Here we model the demand and demand variations for the MR-linac across England. MATERIALS AND METHODS: Initial clinical indications were provided by the MR-linac consortium and introduced into the Malthus radiotherapy clinical decision trees. The Malthus model contains Clinical Commissioning Group (CCG) population, cancer incidence and stage presentation data (for lung and prostate) and simulated the demand for the MR-linac for all CCGs and Radiotherapy Operational Delivery Networks (RODN) across England. RESULTS: Based on the initial target clinical indications, the MR-linac could service 16% of England's fraction burden. The simulated fractions/million population demand/annum varies between 3000 and 10 600 fractions/million at the CCG level. Focussing only on the cancer population, the simulated fractions/1000 cancer cases demand/annum ranges from 1028 to 1195 fractions/1000 cases. If a national average for fractions/million demand was then used, at the RODN level, the variation from actual annual demand ranges from an overestimation of 8400 fractions to an underestimation of 5800 fractions. When using the national average fractions/1000 cases, the RODN demand varies from an overestimation of 3200 fractions to an underestimation of 3000 fractions. CONCLUSIONS: Planning cancer services is complex due to regional variations in cancer burden. The variations in simulated demand of the MR-linac highlight the requirement to use local-level data when planning to introduce a new technology.

Determining the parameter space for effective oxygen depletion for FLASH radiation therapy.

There has been a recent revival of interest in the FLASH effect, after experiments have shown normal tissue sparing capabilities of ultra-high-dose-rate radiation with no compromise on tumour growth restraint. A model has been developed to investigate the relative importance of a number of fundamental parameters considered to be involved in the oxygen depletion paradigm of induced radioresistance. An example eight-dimensional parameter space demonstrates the conditions under which radiation may induce sufficient depletion of oxygen for a diffusion-limited hypoxic cellular response. Initial results support experimental evidence that FLASH sparing is only achieved for dose rates on the order of tens of Gy s-1or higher, for a sufficiently high dose, and only for tissue that is slightly hypoxic at the time of radiation. We show that the FLASH effect is the result of a number of biological, radiochemical and delivery parameters. Also, the threshold dose for a FLASH effect occurring would be more prominent when the parameterisation was optimised to produce the maximum effect. The model provides a framework for further FLASH-related investigation and experimental design. An understanding of the mechanistic interactions producing an optimised FLASH effect is essential for its translation into clinical practice.

In Silico Models of DNA Damage and Repair in Proton Treatment Planning: A Proof of Concept.

There is strong in vitro cell survival evidence that the relative biological effectiveness (RBE) of protons is variable, with dependence on factors such as linear energy transfer (LET) and dose. This is coupled with the growing in vivo evidence, from post-treatment image change analysis, of a variable RBE. Despite this, a constant RBE of 1.1 is still applied as a standard in proton therapy. However, there is a building clinical interest in incorporating a variable RBE. Recently, correlations summarising Monte Carlo-based mechanistic models of DNA damage and repair with absorbed dose and LET have been published as the Manchester mechanistic (MM) model. These correlations offer an alternative path to variable RBE compared to the more standard phenomenological models. In this proof of concept work, these correlations have been extended to acquire RBE-weighted dose distributions and calculated, along with other RBE models, on a treatment plan. The phenomenological and mechanistic models for RBE have been shown to produce comparable results with some differences in magnitude and relative distribution. The mechanistic model found a large RBE for misrepair, which phenomenological models are unable to do. The potential of the MM model to predict multiple endpoints presents a clear advantage over phenomenological models.

Mechanistic modelling supports entwined rather than exclusively competitive DNA double-strand break repair pathway.

Following radiation induced DNA damage, several repair pathways are activated to help preserve genome integrity. Double Strand Breaks (DSBs), which are highly toxic, have specified repair pathways to address them. The main repair pathways used to resolve DSBs are Non-Homologous End Joining (NHEJ) and Homologous Recombination (HR). Cell cycle phase determines the availability of HR, but the repair choice between pathways in the G2 phases where both HR and NHEJ can operate is not clearly understood. This study compares several in silico models of repair choice to experimental data published in the literature, each model representing a different possible scenario describing how repair choice takes place. Competitive only scenarios, where initial protein recruitment determines repair choice, are unable to fit the literature data. In contrast, the scenario which uses a more entwined relationship between NHEJ and HR, incorporating protein co-localisation and RNF138-dependent removal of the Ku/DNA-PK complex, is better able to predict levels of repair similar to the experimental data. Furthermore, this study concludes that co-localisation of the Mre11-Rad50-Nbs1 (MRN) complexes, with initial NHEJ proteins must be modeled to accurately depict repair choice.

Clinically relevant nanodosimetric simulation of DNA damage complexity from photons and protons.

Relative Biological Effectiveness (RBE), the ratio of doses between radiation modalities to produce the same biological endpoint, is a controversial and important topic in proton therapy. A number of phenomenological models incorporate variable RBE as a function of Linear Energy Transfer (LET), though a lack of mechanistic description limits their applicability. In this work we take a different approach, using a track structure model employing fundamental physics and chemistry to make predictions of proton and photon induced DNA damage, the first step in the mechanism of radiation-induced cell death. We apply this model to a proton therapy clinical case showing, for the first time, predictions of DNA damage on a patient treatment plan. Our model predictions are for an idealised cell and are applied to an ependymoma case, at this stage without any cell specific parameters. By comparing to similar predictions for photons, we present a voxel-wise RBE of DNA damage complexity. This RBE of damage complexity shows similar trends to the expected RBE for cell kill, implying that damage complexity is an important factor in DNA repair and therefore biological effect.

Mathematical Modelling for Patient Selection in Proton Therapy.

Proton beam therapy (PBT) is still relatively new in cancer treatment and the clinical evidence base is relatively sparse. Mathematical modelling offers assistance when selecting patients for PBT and predicting the demand for service. Discrete event simulation, normal tissue complication probability, quality-adjusted life-years and Markov Chain models are all mathematical and statistical modelling techniques currently used but none is dominant. As new evidence and outcome data become available from PBT, comprehensive models will emerge that are less dependent on the specific technologies of radiotherapy planning and delivery.

In Silico Non-Homologous End Joining Following Ion Induced DNA Double Strand Breaks Predicts That Repair Fidelity Depends on Break Density.

This work uses Monte Carlo simulations to investigate the dependence of residual and misrepaired double strand breaks (DSBs) at 24 hours on the initial damage pattern created during ion therapy. We present results from a nanometric DNA damage simulation coupled to a mechanistic model of Non-Homologous End Joining, capable of predicting the position, complexity, and repair of DSBs. The initial damage pattern is scored by calculating the average number of DSBs within 70 nm from every DSB. We show that this local DSB density, referred to as the cluster density, can linearly predict misrepair regardless of ion species. The models predict that the fraction of residual DSBs is constant, with 7.3% of DSBs left unrepaired following 24 hours of repair. Through simulation over a range of doses and linear energy transfer (LET) we derive simple correlations capable of predicting residual and misrepaired DSBs. These equations are applicable to ion therapy treatment planning where both dose and LET are scored. This is demonstrated by applying the correlations to an example of a clinical proton spread out Bragg peak. Here we see a considerable biological effect past the distal edge, dominated by residual DSBs.

Tumour Volume and Dose Influence Outcome after Surgery and High-dose Photon Radiotherapy for Chordoma and Chondrosarcoma of the Skull Base and Spine.

AIMS: To evaluate the long-term outcomes of patients with chordoma and low-grade chondrosarcoma after surgery and high-dose radiotherapy. MATERIALS AND METHODS: High-dose photon radiotherapy was delivered to 28 patients at the Neuro-oncology Unit at Addenbrooke's Hospital (Cambridge, UK) between 1996 and 2016. Twenty-four patients were treated with curative intent, 17 with chordoma, seven with low-grade chondrosarcoma, with a median dose of 65 Gy (range 65-70 Gy). Local control and survival rates were calculated using the Kaplan-Meier method. RESULTS: The median follow-up was 83 months (range 7-205 months). The 5 year disease-specific survival for chordoma patients treated with radical intent was 85%; the local control rate was 74%. The 5 year disease-specific survival for chondrosarcoma patients treated with radical intent was 100%; the local control rate was 83%. The mean planning target volume (PTV) was 274.6 ml (median 124.7 ml). A PTV of 110 ml or less was a good predictor of local control, with 100% sensitivity and 63% specificity. For patients treated with radical intent, this threshold of 110 ml or less for the PTV revealed a statistically significant difference when comparing local control with disease recurrence (P = 0.019, Fisher's exact test). Our data also suggest that the probability of disease control may be partly related to both target volume and radiotherapy dose. CONCLUSION: Our results show that refined high-dose photon radiotherapy, following tumour resection by a specialist surgical team, is effective in the long-term control of chordoma and low-grade chondrosarcoma, even in the presence of metal reconstruction. The results presented here will provide a useful source for comparison between high-dose photon therapy and proton beam therapy in a UK setting, in order to establish best practice for the management of chordoma and low-grade chondrosarcoma.

Automatic cell detection in bright-field microscopy for microbeam irradiation studies.

Automatic cell detection in bright-field illumination microscopy is challenging due to cells' inherent optical properties. Applications including individual cell microbeam irradiation demand minimisation of additional cell stressing factors, so contrast-enhancing fluorescence microscopy should be avoided. Additionally, the use of optically non-homogeneous substrates amplifies the problem. This research focuses on the design of a method for automatic cell detection on polypropylene substrate, suitable for microbeam irradiation. In order to fulfil the relative requirements, the Harris corner detector was employed to detect apparent cellular features. These features-corners were clustered based on a dual-clustering technique according to the density of their distribution across the image. Weighted centroids were extracted from the clusters of corners and constituted the targets for irradiation. The proposed method identified more than 88% of the 1,738 V79 Chinese hamster cells examined. Moreover, a processing time of 2.6 s per image fulfilled the requirements for a near real-time cell detection-irradiation system.

Quantifying uncertainty in radiotherapy demand at the local and national level using the Malthus model.

The Malthus programme produces a model for the local and national level of radiotherapy demand for use by commissioners and radiotherapy service leads in England. The accuracy of simulation is dependent on the population cancer incidence, stage distribution and clinical decision data used by the model. In order to quantify uncertainty in the model, a global sensitivity analysis of the Malthus model was undertaken. As predicted, key decision points in the model relating to stage distribution and indications for surgical or non-surgical initial management of disease were observed to yield the strongest effect on simulated radiotherapy demand. The proportion of non-small cell lung cancer patients presenting with stage IIIB/IV disease had the largest effect on fraction burden in the four most common cancer types treated with radiotherapy, where a 1% change in stage IIIb/IV disease yielded a 1.3% change in fraction burden for lung cancer patients. A 1% change in mastectomy rate yielded a 0.37% change in fraction burden for breast cancer patients. The model is also highly sensitive to changes in the radiotherapy indications in colon and gastric cancer. Broadly, the findings of the sensitivity analysis mirror those previously published by other groups. Sensitivity analysis of the local-level population and cancer incidence data revealed that the cancer registration rate in the 50-64 year female population had the highest effect on simulation results. The analysis reveals where additional effort should be undertaken to provide accurate estimates of important parameters used in radiotherapy demand models.

Environmental & economic life cycle assessment of current & future sewage sludge to energy technologies.

The UK Water Industry currently generates approximately 800GWh pa of electrical energy from sewage sludge. Traditionally energy recovery from sewage sludge features Anaerobic Digestion (AD) with biogas utilisation in combined heat and power (CHP) systems. However, the industry is evolving and a number of developments that extract more energy from sludge are either being implemented or are nearing full scale demonstration. This study compared five technology configurations: 1 - conventional AD with CHP, 2 - Thermal Hydrolysis Process (THP) AD with CHP, 3 - THP AD with bio-methane grid injection, 4 - THP AD with CHP followed by drying of digested sludge for solid fuel production, 5 - THP AD followed by drying, pyrolysis of the digested sludge and use of the both the biogas and the pyrolysis gas in a CHP. The economic and environmental Life Cycle Assessment (LCA) found that both the post AD drying options performed well but the option used to create a solid fuel to displace coal (configuration 4) was the most sustainable solution economically and environmentally, closely followed by the pyrolysis configuration (5). Application of THP improves the financial and environmental performance compared with conventional AD. Producing bio-methane for grid injection (configuration 3) is attractive financially but has the worst environmental impact of all the scenarios, suggesting that the current UK financial incentive policy for bio-methane is not driving best environmental practice. It is clear that new and improving processes and technologies are enabling significant opportunities for further energy recovery from sludge; LCA provides tools for determining the best overall options for particular situations and allows innovation resources and investment to be focused accordingly.

The Malthus Programme: developing radiotherapy demand models for breast and prostate cancer at the local, regional and national level.

AIMS: The Malthus Programme has delivered a tool for modelling radiotherapy demand in England. The model is capable of simulating demand at the local level. This article investigates the local and regional level variation in predicted demand with respect to Breast and Prostate cancer, the two tumour types responsible for the majority of radiotherapy treatment workload in England. MATERIALS AND METHODS: Simulations were performed using the Malthus model, using base population incidence data for the period from 2007-2009. Simulations were carried out at the level of Primary Care Trusts, Cancer Networks, and nationwide, with annual projections for 2012, 2016 and 2020. Benchmarking was undertaken against previously published models from the UK, Canada and Australia. RESULTS: For breast cancer, the fraction burden for 2012 varied from 5537 fractions per million in Tower Hamlets PCT to 18 896 fractions per million in Devon PCT (national mean - 13 592 fractions per million). For prostate cancer, the fraction burden for 2012 varied from 4874 fractions per million in Tower Hamlets PCT to 23 181 fractions per million in Lincolnshire PCT (national mean - 15 087 fractions per million). Predictions of population growth by age cohort for 2016 and 2020 result in the regional differences in radiotherapy demand becoming greater over time. Similar effects were also observed at the level of the cancer network. CONCLUSIONS: Our model shows the importance of local population demographics and cancer incidence rates when commissioning radiotherapy services.

Radiotherapy demand and activity in England 2006-2020.

AIMS: This paper compares the predictions of radiotherapy demand for England from the Malthus model with those from the earlier National Radiotherapy Advisory Group (NRAG) model, from the international literature and also with observed radiotherapy usage in England as a whole as recorded in the English radiotherapy dataset (RTDS). MATERIALS AND METHODS: We reviewed the evidence base for radiotherapy for each type and stage of cancer using national and international guidelines, meta-analyses, systematic reviews and key clinical trials. Twenty-two decision trees were constructed and radiotherapy demand was calculated using English cancer incidence data for 2007, 2008 and 2009, accurate to the Primary Care Trust (PCT) level (population 91,500-1,282,384). The stage at presentation was obtained from English cancer registry data. In predictive mode, the model can take account of changes in cancer incidence as the population grows and ages. RESULTS: The Malthus model indicates reduced indications for radiotherapy, principally for lung cancer and rarer tumours. Our estimate of the proportion of patients who should receive radiotherapy at some stage of their illness is 40.6%. This is lower than previous estimates of about 50%. Nevertheless, the overall estimate of demand in terms of attendances is similar for the NRAG and Malthus models. The latter models that 48,827 attendances should have been delivered per million population in 2011. National data from RTDS show 32,071 attendances per million in 2011. A 50% increase in activity would be required to match estimated demand. This underprovision extends across all cancers and represents reduced access and the use of dose fractionation at odds with international norms of evidence-based practice. By 2016, demand is predicted to grow to about 55,206 attendances per million and by 2020 to 60,057. DISCUSSION: Services have increased their activity by 14% between 2006 and 2011, but estimated demand has increased by 11%. Access remains low and English radiotherapy dose fractionation still does not comply with international evidence-based practice.

A novel algorithm for the morphometric assessment of radiotherapy treatment planning volumes.

Quantitative assessment of target volume contouring in radiotherapy treatment planning is an important aspect of quality assessment and educational exercises. The Conformity Index (CI) is a volume-based statistic frequently used for this purpose. Although the CI is relatively simple to understand and can be calculated using most treatment planning systems, it does not provide any information on the differences in shape between the two volumes. We present a new morphometric (shape-based) statistic known as the "mean distance to conformity" (MDC). For a specific volume that is being evaluated against a reference volume, the MDC represents the average distance that all outlying points in the volume must be moved in order to achieve perfect conformity with the reference volume. The MDC comprises a component related to under-contouring (where the evaluation volume is smaller than the reference volume) and a component related to over-contouring (where the evaluation extends beyond the reference volume). Furthermore, voxel-by-voxel information on conformity errors can also be displayed using a volume-error histogram. Calculation of MDC statistics is achieved using a three-dimensional grid search algorithm. By using a range of scenarios comprising both theoretical and actual clinical volumes, we demonstrate the increased utility of the MDC for the detection of contouring errors.

A computer model of the Bystander effect: effects of individual behaviours on the population response.

A computer program was written to test assumptions on the mechanisms of response of cells to radiation. Current assumptions were implemented in the model and simulations were run to predict the survival of the hamster cell line V79 to irradiation with focused C(K) X-rays, 250 keV X-rays or 3.2 MeV protons. The model could reproduce the different types of response and support the idea that the response at low doses is non-linear and may be independent of LET.

Cellular automaton model of cell response to targeted radiation.

It has been shown that the response of cells to low doses of radiation is not linear and cannot be accurately extrapolated from the high dose response. To investigate possible mechanisms involved in the behaviour of cells under very low doses of radiation, a cellular automaton (CA) model was created. The diffusion and consumption of glucose in the culture dish were computed in parallel to the growth of cells. A new model for calculating survival probability was introduced; the communication between targeted and non-targeted cells was also included. Early results on the response of non-confluent cells to targeted irradiation showed the capability of the model to take account for the non-linear response in the low-dose domain.

Early radiotherapy dose response and lack of hypersensitivity effect in normal brain tissue: a sequential dynamic susceptibility imaging study of cerebral perfusion.

AIMS: To determine if magnetic resonance perfusion markers can be used as an analytical marker of subclinical normal brain injury after radiotherapy, by looking for a dose-effect relationship. MATERIALS AND METHODS: Four patients undergoing conformal radiotherapy to 54Gy in 30 fractions for low-grade gliomas were imaged with conventional T(2)-weighted and fluid attenuated inversion recovery imaging as well as dynamic contrast susceptibility perfusion imaging. Forty regions of interest were determined from the periventricular white matter. All conventional sequences were examined for evidence of radiation-induced changes. Patients were imaged before radiotherapy, after one fraction, at the end of treatment and then at 1 and 3 months from the end of radiotherapy. For each region the relative cerebral blood volume (rCBV), relative cerebral blood flow (rCBF) and mean transit time (MTT) expressed as a ratio of the baseline value, and radiotherapy dose were determined. RESULTS: Of the 40 regions, seven occurred within the gross tumour volume and a further four occurred in regions later infiltrated by tumour, and were thus excluded. Regions within the 80% isodose showed a reduction in rCBV and rCBF over the 3 month period. There was no significant alteration in rCBV or rCBF in regions outside the 60% isodose (i.e. <32Gy). MTT did not alter in any region. There seemed to be a threshold effect at 132 days from the end of radiotherapy of 47% (standard error of the mean 11.5, about 25.4Gy) for rCBV and 59% (standard error of the mean 14.2, about 31.9Gy) for rCBF. CONCLUSIONS: There was a dose-related reduction in rCBV and rCBF in normal brain after radiotherapy at higher dose levels. Although this study used a limited number of patients, it suggests that magnetic resonance perfusion imaging seems to act as a marker of subclinical response of normal brain and that there is an absence of an early hypersensitivity effect with small doses per fraction. Further studies are required with larger groups of patients to show that these results are statistically robust.

Mathematical modelling of survival of glioblastoma patients suggests a role for radiotherapy dose escalation and predicts poorer outcome after delay to start treatment.

AIMS: The outcome of patients with glioblastoma (GBM) remains extremely poor. We have developed a mathematical model, using pathological and radiation biology concepts, to assess the detrimental effect of delay to start radiotherapy, the possible benefit from dose escalation, and to extract biological data from clinical data. MATERIALS AND METHODS: Survival data were available for 154 adult patients with GBM treated in our centre with curative intent to a dose of 60 Gy in 30 fractions between 1996 and 2002. Survival data for 129 patients from the 60 Gy arm of the MRC BR02 randomised trial of radiotherapy dose were obtained for comparison. The model generates the equivalent of individual patients with a brain tumour, and produces an explicit outcome, either death or survival. The tumour, assumed to be growing exponentially, causes normal cell damage in the brain, and death occurs when the number of normal brain cells falls below a critical level. The outcome for an individual patient is determined by values of the variables assigned by the model. Parameters for the single patient include tumour doubling time, surviving fraction of tumour cells after each fraction of radiotherapy, and a waiting time from presentation to the start of radiotherapy. A surrogate for performance status is implemented, using a rule that rejects patients whose tumours are too advanced at presentation to be suitable for radical radiotherapy. Values for the parameters that determine individual patient outcome are randomly assigned from a set of probability distributions, using Monte Carlo simulation. The simulation constructs survival results for a population, typically 2000 individuals. The descriptors of the probability distributions that are used to determine the parameters that define the patient characteristics are adjusted to optimise the fit of the modelled population to real clinical data, using a combination of folding polygon and simulated annealing techniques. RESULTS: The model fits the clinical data well. The results suggest that the surviving fraction of tumour cells after a radiation dose of 2 Gy (SF2) does influence patient outcome. The mean in vivo SF2 for the Addenbrooke's data is 0.80, implying that hypoxia is a serious problem in radiotherapy for GBM. The Addenbrooke's data suggest a mean tumour doubling time of 24 days, so that a delay to start radiotherapy would be expected to have an adverse effect. Considering patients by treatment intent, median survival plummets as delay increases, and almost no patients survive long term after a 70-day delay. Radiotherapy dose escalation has an important predicted effect on survival. Assuming that the treatment could be delivered safely, a dose of 74 Gy, given at 2 Gy/fraction, would extend the survival of all patients. The proportion of long-term survivors would increase, from 2.4% with 60 Gy, to 6.4% with 74 Gy. The model can be used to derive gamma50, which has a value of 0.42, lower than the typical value of 1-2. CONCLUSION: Using the model, we have extracted biological information from clinical data. The model could be used to assess the potential benefit, or lack of benefit, from a proposed radiotherapy trial, and to estimate the necessary size. It shows that a single modality is unlikely to achieve a major improvement in long-term survival, although radiotherapy dose escalation should have a role, provided it can be given safely. The model could be extended to include chemotherapy, bio-reductive drugs, or gene therapy.