Clinical Adaptive Radiation Transport Algorithms (CARTA)

临床自适应辐射传输算法 (CARTA)

• 批准号: EP/R030707/1
• 负责人: Paul Houston
• 金额: $ 40.73万
• 依托单位: University of Nottingham
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FR030707%2F1
• 关键词: Clinical; Adaptive; Radiation; Transport; Algorithms

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.

癌症是世界上导致死亡的主要原因之一。仅在英国，每天就会诊断出约 1000 例病例，根据 NHS 的数据，近一半的癌症治疗患者将放射治疗作为其治疗计划的一部分。对于给定的射束配置，任何有效的治疗计划系统的一个组成部分都是快速、准确和稳健地预测输送到肿瘤、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出的，如 CT 图像数据所示，并由辐射与组织之间的物理相互作用的适当模型控制。当前的黄金标准是蒙特卡罗 (MC) 方法，该方法考虑了穿过组织的许多粒子历史。然而，MC 模拟中的“误差”减少得非常缓慢：在精度上添加一个额外的小数位需要花费 100 倍的时间，这意味着生成足够准确的预测实在太慢了。这个问题通常通过利用更简单、不太现实的模型来解决，这些模型可以非常快速地进行模拟；然而，这种简化物理模型的验证通常仍然涉及使用 MC 进行基准测试。显然，这不是一个令人非常满意的情况。事实上，迫切需要开发下一代计算工具，它们不仅比 MC 更高效，而且能够提供有关数值解中误差大小的可靠信息，从而为这些安全关键型应用提供严格的解验证。随机 MC 算法的替代方案是线性玻尔兹曼传输方程 (LBTE)；在这里，辐射被视为连续量，用数学表达式描述其产生、“流”过患者以及被患者吸收。这种吸收很重要：在正确的位置发生足够的吸收可以实现所需的肿瘤控制，但是在其他位置吸收过多可能会导致副作用/并发症。 LBTE 可以直接离散化以产生方便的计算机表示，与 MC 相比，这导致了另一种近似，可以直接利用底层微分算子的平滑性。通过这种方式，相对于 MC 算法所需的计算量，可以以更有效的方式控制数值误差，而 MC 算法不利用底层解析解的平滑性。我们希望解决这种方法中的关键挑战：有效处理 LBTE 的高维性质和人体的几何复杂性。此类方法已在医学物理界得到应用，显示出巨大的前景，但它们仍然相对较新，尚未利用可用于提高准确性和效率的全套技术，并且嵌入专有软件中。我们建议开发精确、高效和鲁棒的算法来解决 LBTE，使用非常适合此类问题且适合自适应计算的方法。因此，我们将开发一种优化配置的算法，以利用平滑区域，但能够在组织特性快速变化时适应处理区域，目标是有效近似（临床）感兴趣的规定量，例如器官剂量。我们将采用的基础数值方法自然会提供一个框架，在该框架内可以量化与指定物理的精确表示相比的误差，从而可以实现严格的解决方案验证。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、全面的测试，并确保其开发以最终必须遵循的临床协议为指导。

项目成果

High-order Space-Angle-Energy Discontinuous Galerkin Finite Element Methods on Polytopic Meshes for the Linear Boltzmann Transport Problem

线性玻尔兹曼输运问题多面体网格的高阶空间-角度-能量不连续伽辽金有限元方法

• 期刊: Journal of Scientific Computing (submitted)
• 作者: Paul Houston

Two-grid $hp$-version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes

聚集粗网格上拟线性椭圆偏微分方程的两网格 $hp$ 版本不连续 Galerkin 有限元方法

• DOI: 10.48550/arxiv.2112.04540
• 发表时间: 2021
• 作者: Congreve S

Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods

• DOI: 10.1142/s0218202521500172
• 发表时间: 2020-05
• 期刊: ArXiv
• 作者: A. Cangiani;E. Georgoulis;Oliver J. Sutton

Quadrature-Free Polytopic Discontinuous Galerkin Methods for Transport Problems

用于解决输运问题的无正交多面不连续伽辽金方法

• DOI: 10.48550/arxiv.2310.10406
• 发表时间: 2023
• 作者: Radley T

Residual-based a posteriori error estimates for $\mathbf{hp}$-discontinuous Galerkin discretisations of the biharmonic problem

双调和问题的 $mathbf{hp}$-不连续伽辽金离散的基于残差的后验误差估计

• DOI: 10.48550/arxiv.2009.14140
• 发表时间: 2020
• 作者: Dong Z