Clinical Adaptive Radiation Transport Algorithms (CARTA)

癌症是世界上主要的死亡原因之一。仅在英国，每天就有大约1000例确诊病例，根据英国国民健康保险制度的数据，近一半的癌症患者在治疗计划中接受了放射治疗。任何有效的治疗计划系统的一个组成部分是，对于给定的射束配置，快速、准确和稳健地预测传输到肿瘤、周围组织和重要器官的辐射剂量分布。这些预测是通过模拟辐射通过患者身体的传输而得到的，如CT图像数据所表示的，受辐射与组织之间的物理相互作用的适当模型的支配。目前的黄金标准是蒙特卡罗(MC)方法，它考虑了许多穿过组织的粒子历史。然而，MC模拟中的“误差”下降得非常慢：在精度上多加一个小数位需要100倍的时间，这意味着产生足够准确的预测实在太慢了。这个问题通常是通过开发更简单、更不现实的模型来解决的，这些模型可以非常快速地进行模拟；然而，验证这种简化的物理模型通常仍然需要与MC进行基准测试。显然，这不是一个非常令人满意的情况；事实上，迫切需要开发下一代计算工具，这些工具不仅比MC更有效，而且提供关于数值解中误差大小的可靠信息，从而为这些安全关键应用提供严格的解验证。除了随机MC算法，还有线性玻尔兹曼传输方程(LBTE)；这里，辐射被视为一个连续量，其数学表达式描述了辐射的产生及其通过患者的吸收。这种吸收很重要：在正确的位置发生足够的吸收会导致所需的肿瘤控制，然而，在其他位置吸收太多可能会导致副作用/并发症。与MC相比，LBTE可以直接离散化以产生方便的计算机表示，这导致可以直接利用基础微分算子的光滑性的另一种近似。这样，相对于MC算法所需的计算工作量，可以以更有效的方式控制数值误差，因为MC算法不利用基本解析解的光滑性。我们希望解决这一方法中的关键挑战：有效地处理LBTE的高维性质和人体的几何复杂性。这种类型的方法已经在医学物理界使用，显示出巨大的前景，但它们仍然是相对较新的，尚未利用可用于提高精度和效率的各种技术，并嵌入到专有软件中。我们建议开发精确、高效和健壮的算法来解决LBTE，使用理想的适合于这类问题的方法，并且服从自适应计算。因此，我们将开发一种优化配置的算法，以利用平滑区域，并且能够适应组织属性快速变化时的处理区域，目标是有效地近似指定的(临床)感兴趣的量，例如，器官剂量。我们将采用的基本数值方法自然将提供一个框架，在该框架内，相对于特定物理的精确表示的误差可以被量化，从而可以实现严格的解验证。此外，我们将与Altnagelvin医院合作，确保我们的软件与最终用户合作，针对现有模拟软件进行公平和全面的测试，并确保其开发遵循最终必须遵循的临床方案。

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.