Optimizing advanced stereotactic radiosurgery techniques for brain cancer treatment

脑癌是加拿大青少年和年轻人癌症死亡的第二大原因（加拿大癌症协会，2013年）。放射外科（RS）是一种常见的治疗脑部和颅底癌性肿瘤的技术，而RS治疗的准确性对成功根除癌症至关重要。由于辐射对健康组织和癌变组织都有损害，高质量的放射治疗计划必须避免向健康组织提供过量剂量，同时向肿瘤（通常位于脑干附近）提供大剂量。与其他类型的放射治疗不同，放射治疗通常由一种显著放射剂量的治疗组成，而不是许多小剂量的治疗（称为部分治疗）。Elekta伽玛刀（PFX）是最先进的RS放射输送装置，每年用于治疗约50,000名患者（Elekta AB, 2013）。在PFX治疗中，患者躺在沙发上，周围有八排放射源（称为扇区），所有放射源都瞄准肿瘤内的一个单一位置（称为等中心）。然后，沙发移动到肿瘤的不同位置，然后到另一个等中心，等等，直到目标被治疗；这个过程被称为“步进投篮”。在每个等心，扇形可以发射三种不同直径的辐射光束（称为准直器尺寸），以在任何等心产生任何辐射剂量沉积。躺椅位置和准直器配置的选择可以形成优化治疗质量的数学模型。目前，临床医生手动选择等中心和准直器，这可能导致次优治疗和较长的计划时间。此外，步进射击过程可能会产生较长的治疗时间，并限制了治疗大型目标的能力。因此，临床对过渡到“连续路径”治疗有很大的兴趣，在这种治疗中，随着设备的移动，辐射不断地传递（就像用辐射涂抹肿瘤）。PFX用于多组分RS （MF-RS）也有临床兴趣，它具有挑战性的剂量均匀性要求，不像单组分RS (SF-RS)，其目标剂量可高达处方剂量的两倍。使用MF-RS，必须解决器官运动和设置误差。也有人认为，即使在SF-RS中也存在少量的器官运动。为了解决计划治疗中的这些挑战，该研究项目将在数学建模和优化领域开发方法和工具，为接受SF-RS和MF-RS的患者提供高质量的个性化癌症护理。这项研究将允许使用PFX更准确地消除肿瘤，因此有可能挽救许多生命，并使许多患者免于因次优治疗而产生的副作用。此外，使用连续路径治疗将允许治疗更大的靶点，扩大有资格接受PFX治疗的人群，为临床医生提供更多的治疗选择，并增加PFX设备的利用率。此外，连续处理将比分步射击处理更快地交付，从而允许PFX单元的更高吞吐量。因此，加拿大人将受益于癌症治疗健康结果的改善和昂贵医疗设备利用率的提高。研究领域将受益于在数学模型中模拟连续运动的技术的发展，以及在基于凸惩罚的优化模型中纳入特定尺寸不确定性的新技术。生成覆盖封闭体积的连续路径的方法在机器人和其他领域都有应用。

Brain cancer is the second-highest cause of cancer death in Canadian adolescents and young adults Canadian Cancer Society, 2013). Radiosurgery (RS) is a common treatment technique for cancerous tumours in the brain and base of the skull, and the accuracy of the RS treatment is critical to successful cancer eradication. Because radiation is damaging to healthy tissue as well as cancerous tissue, high-quality RS treatment plans must avoid delivering excessive dose to healthy tissue while simultaneously delivering a large dose to tumours, which are commonly positioned adjacent to the brainstem. Unlike other types of radiation therapy, RS usually consists of one treatment of significant radiation dose, rather than many treatments (called fractions) of small dose.The Elekta Gamma Knife Perfexion (PFX) is the state-of-the-art radiation delivery unit for RS, used to treat an estimated 50,000 patients each year (Elekta AB, 2013). In PFX, the patient lies on a couch, surrounded by eight banks of radiation sources (called sectors) all aimed at a single location (called an isocentre) inside a tumour. The couch then moves to irradiate a different location in the tumour, and then to another isocentre, etc., until the target is treated; this process is called “step-and-shoot”. At each isocentre, the sectors can emanate radiation beams of three different diameters (called collimator sizes) to create any radiation dose deposition at any isocentre. The selection of couch positions and collimator configurations can be formulated as a mathematical model to optimize treatment quality. Currently, clinicians manually select isocentres and collimators, which can lead to sub-optimal treatments and long planning times. Additionally, the step-and-shoot process can yield lengthy treatment times and limits the ability to treat large targets. Thus, there is significant clinical interest in transitioning to “continuous path” treatments, where radiation is delivered continuously while the device moves (like painting the tumour with radiation). There is also clinical interest in using PFX for multi-fraction RS (MF-RS), which has challenging dose homogeneity requirements, unlike single-fraction RS (SF-RS), where target dose can be up to twice the prescription dose. With MF-RS, organ motion and setup errors must be addressed. It is also believed that small amounts of organ motion are present even in SF-RS.To address these challenges in planning treatments, this research program will develop methods and tools within the fields of mathematical modelling and optimization to provide high-quality, personalized cancer care for patients receiving SF-RS and MF-RS with PFX. This research will allow more accurate elimination of tumours using PFX, and thus has the potential to save many lives and spare many patients from side effects arising from suboptimal treatments. Further, the use of continuous path treatments will allow larger targets to be treated, expanding the population who is eligible to be treated by PFX, giving clinicians more treatment options, and increasing utilization of PFX equipment. Additionally, continuous treatments will be much faster to delivery than step-and-shoot treatments, allowing for more throughput on PFX units. Thus, Canadians will benefit from both improved health outcomes in cancer treatments and improved utilization of costly healthcare equipmentThe research field will benefit from the development of techniques to model continuous motion within mathematical models, as well as new techniques to incorporate dimension-specific uncertainties within convex penalty-based optimization models. The methods to generate continuous paths that cover a closed volume have applications in robotics and other areas.