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)。放射外科是治疗脑肿瘤和颅底肿瘤的常用方法，放射外科治疗的准确性是肿瘤根治成功的关键。由于辐射对健康组织和癌症组织都有损害，高质量的RS治疗计划必须避免向健康组织提供过量剂量，同时向肿瘤提供大剂量辐射，肿瘤通常位于脑干附近。与其他类型的放射治疗不同，RS通常包括一个大剂量的放射治疗，而不是许多小剂量的治疗(称为分次治疗)。 Elekta伽玛刀Perfexion(PFX)是最先进的RS放射传输设备，每年用于治疗约50,000名患者(Elekta AB，2013)。在PFX中，患者躺在沙发上，周围有八组放射源(称为扇区)，这些放射源都对准肿瘤内的一个位置(称为等中心)。然后，沙发移动，照射肿瘤中的不同位置，然后移动到另一个等中心，等等，直到靶子被治疗；这个过程被称为“分步拍摄”。在每个等中心，扇区可以发射三种不同直径的辐射束(称为准直器尺寸)，以在任何等中心产生任何辐射剂量沉积。床位和准直器配置的选择可以表示为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规划时间。此外，分步发射过程可能会产生较长的治疗时间，并限制治疗大靶点的能力。因此，临床上对过渡到“连续路径”治疗有很大的兴趣，在这种治疗中，放射在设备移动的同时持续传递(就像用辐射涂抹肿瘤一样)。临床上也有兴趣将PFX用于多组分RS(MF-RS)，与单组分RS(SF-RS)不同，MF-RS具有挑战性的剂量均一性要求，其目标剂量可高达处方剂量的两倍。对于MF-RS，必须解决器官运动和设置错误。人们还认为，即使在SF-RS中也存在少量的器官运动。 为了应对计划治疗方面的这些挑战，这项研究计划将在数学建模和优化领域开发方法和工具，为使用PFX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人的生命，使许多患者免于因次优治疗而产生的副作用。此外，连续路径治疗的使用将允许更大的靶点被治疗，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，连续治疗将比分步注射治疗更快地交付，从而允许在PFX单元上获得更大的吞吐量。因此，加拿大人将受益于癌症治疗中健康结果的改善和昂贵医疗设备的利用 研究领域将受益于在数学模型中对连续运动建模的技术的发展，以及将特定维度的不确定性纳入基于凸罚的优化模型的新技术。生成覆盖闭合体积的连续路径的方法在机器人学和其他领域有应用。

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 equipment The 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.