Clinical Adaptive Radiation Transport Algorithms (CARTA)

Cancer is one of the leading causes of death in the world. In the UK alone, around 1000 cases are diagnosed every day and, according to the NHS, almost half of those treated for cancer have radiotherapy as part of their treatment plan. An integral part of any effective treatment planning system is rapid, accurate, and robust prediction of the distribution of radiation dose delivered to the tumour, the surrounding tissue, and vital organs, for a given beam configuration. These predictions are derived by simulating radiation transport through the patient's body, as represented by CT image data, governed by an appropriate model of the physical interaction between the radiation and the tissue.

The current gold standard is the Monte Carlo (MC) approach, which considers many particle histories travelling through the tissue. However, the `error' in the MC simulations decreases very slowly: adding an extra decimal place to the accuracy takes 100 times as long, which means that the generation of sufficiently accurate predictions is simply too slow. This issue is commonly addressed by exploiting simpler, less realistic models, which can be very quickly simulated; however, validation of such reduced-physics models still typically involves benchmarking with MC. Clearly, this is not a very satisfactory situation; indeed, there is an urgent need to develop the next generation of computational tools, which are not only more efficient than MC, but provide reliable information regarding the size of the error in the numerical solution, thereby providing rigorous solution verification for these safety-critical applications.

An alternative to stochastic MC algorithms, is the linear Boltzmann transport equation (LBTE); here, radiation is treated as a continuous quantity with mathematical expressions describing its generation and its `flow' through and absorption by the patient. This absorption is important: sufficient absorption occurring in the correct location leads to the desired tumour control, however, too much in other places can lead to side-effects/complications. The LBTE can be directly discretized to yield a convenient computer representation which, in contrast to MC, leads to an alternative approximation which may directly exploit the smoothness of the underlying differential operator. In this way, the numerical error can be controlled in a much more efficient manner, relative to the computational effort required by MC algorithms, which does not exploit the smoothness of the underlying analytical solution. We wish to address the key challenges in this approach: to deal efficiently with the high-dimensional nature of the LBTE and the geometrical complexity of the human body. Methods of this type have been employed in the medical physics community, showing great promise, but they are still relatively new, have yet to take advantage of the full range of techniques which can be used to improve accuracy and efficiency, and are embedded in proprietary software.

We propose to develop precise, efficient, and robust algorithms for solving the LBTE, using methods ideally suited to problems of this type and which are amenable to adaptive computation. We will therefore develop an algorithm optimally configured to exploit smooth regions and yet able to adapt to handle regions when tissue properties change rapidly, targeted at efficient approximation of prescribed quantities of (clinical) interest, e.g., dose-to-organ. The underlying numerical method we will employ will naturally provide a framework within which errors compared to an exact representation of the specified physics can be quantified, so that rigorous solution verification can be achieved. Furthermore, we will work with Altnagelvin Hospital, to ensure that our software is tested fairly and comprehensively against existing simulation software in collaboration with end-users, and that its development is guided by the clinical protocols it would ultimately have to follow.

Economic and Societal:

According to Cancer Research UK, someone is diagnosed with cancer in the UK every 2 minutes, and someone dies of it every 4 minutes. Quite apart from the human cost, the consequent economic losses due to early death, time off work, unpaid care and national healthcare was estimated to be more than £15 billion annually by an Oxford University study conducted in 2012. Radiotherapy is used in the treatment of nearly half of cancer patients in the UK and a crucial element in planning the most appropriate delivery strategy is the ability to predict the distribution of radiation dose that will actually be delivered to the patient. Our goal is to improve the accuracy with which these predictions can be made within the limited timescales inherent in clinical decision-making, and hence improve the chances of successful treatment by designing optimized, patient-specific, radiation delivery plans. We plan to maximize our chances of success by collaborating throughout the project with our clinical partners at Altnagelvin Hospital.

Although we will focus on radiotherapy applications, the methods developed can impact any societal activity where one needs to know the transport of ionizing radiation through matter, including detector development, medical imaging, radiation sterilization, civil nuclear waste handling, radiation protection and space electronics.

Academic and Clinical:

Academic and clinical impact will follow from the development of freely available software for the adaptive approximation of the high-dimensional hyperbolic integro-partial differential equations governing radiation transport in complex geometries, tailored to provide optimal computation of radiation dose distributions to pre-specified regions of the body. The academic beneficiaries of the new algorithms and analysis are summarized in the appropriate section, but the availability of fast, robust software with rigorous error control would broaden the impact to other communities in which safety-critical applications related to radiation are the norm, such as the nuclear industry. The primary aim is, however, to link with clinical radiotherapists and radiation physicists working in healthcare. This will be facilitated by working with Altnagelvin Hospital, carrying out our research alongside the Centre for Advanced and Interdisciplinary Radiation Research (CAIRR) at Belfast, and liaising with the STFC's Advanced Radiotherapy Network+ to organize a Future-Users Workshop involving patient representatives and equipment vendors.

A project of this type also has the advantage of training young researchers to work at the interface between disciplines. In particular, the PDRAs employed on this grant would gain experience of tailoring academic research in mathematics and physics for the benefit of a tangible and important real-life application, under the guidance of the end-users. This will develop researchers whose expertise in bridging the gap between academia (theoretical numerical analysis) and the clinic (mock commissioning of software in a clinical environment) will be invaluable to subsequent employers. Furthermore, smaller-scale projects will be advertised to attract PhD, Masters, and Undergraduate students to work in this area and develop similar skills.