A shortest path-based approach to the multileaf collimator sequencing problem

AbstractThe multileaf collimator sequencing problem is an important component in effective cancer treatment delivery. The problem can be formulated as finding a decomposition of an integer matrix into a weighted sequence of binary matrices whose rows satisfy a consecutive ones property. Minimising the cardinality of the decomposition is an important objective and has been shown to be strongly NP-hard, even for a matrix restricted to a single column or row. We show that in this latter case it can be solved efficiently as a shortest path problem, giving a simple proof that the one-row problem is fixed-parameter tractable in the maximum intensity. We develop new linear and constraint programming models exploiting this result. Our approaches significantly improve the best known for the problem, bringing real-world sized problem instances within reach of exact algorithms

Robust Direct Aperture Optimization Methods for Cardiac Sparing in Left-Sided Breast Cancer Radiation Therapy

Designing conformal and equipment-compatible radiation therapy plans is essential for ensuring high-quality treatment outcomes for cancer patients. Intensity modulated radiation therapy (IMRT) is a commonly-used method of radiation delivery for cancer patients, wherein beams of radiation are individually contoured to cover a patient’s tumour cells while avoiding healthy cells and organs. In IMRT for left-sided breast cancer, the goal is to irradiate all cells in the breast tissue while avoiding the neighbouring, and extremely radiation-sensitive, heart cells. To add to the complexity of this treatment, the entire dose must be delivered while the patient is breathing, causing the location of the heart and target organs to move and deform unpredictably. The search for a plan that is of the highest quality for a specified set of parameters is called treatment plan optimization. One method of treatment plan optimization that provides an optimal radiation distribution, even under the worst-case realization of a patient’s motion uncertainty, uses a framework called robust optimization. A drawback of using this robust optimization framework, however, is that it does not immediately output physically deliverable IMRT plans. Rather, a subsequent, non-trivial post-processing phase must be applied to the output intensity distributions in order to generate an equipment-compatible plan; a process which can substantially degrade the treatment quality. In this thesis, a holistic approach that combines enforcement of delivery constraints with robust optimization is introduced. The process for creating deliverable plans is called direct aperture optimization (DAO), and the combined model is called robust DAO (RDAO). Novel modelling strategies for integrating the DAO requirements into a robust framework are presented, leading to a large-scale difficult-to-solve mixed integer programming problem. To contend with the complexity of the problem, additional modelling approaches are suggested for improving solution efficiency. These approaches include a hybrid heuristic-optimization technique, which provides good quality, but non-optimal treatment plans. Clinicians may use the output of this hybrid technique as is, or apply it as a warm start for the RDAO model. The models are implemented in C++ and CPLEX and results are presented, first using a one-dimensional phantom, and then a three-dimensional clinical patient dataset. While the full RDAO model is quite time-consuming to run, high-quality plans are ultimately produced. These plans are both clinically deliverable and mitigate the risk of underdosing a patient’s cancerous cells under motion uncertainty, demonstrating their value over plans that did not account for motion uncertainty

Applications of mathematical network theory

This thesis is a collection of papers on a variety of optimization problems where network structure can be used to obtain efficient algorithms. The considered applications range from the optimization of radiation treatment plkans in cancer therapy to maintenance planning for maximizing the throughput in bulk good supply chains

Beam selection for stereotactic ablative radiotherapy using Cyberknife with multileaf collimation.

The Cyberknife system (Accuray Inc., Sunnyvale, CA) enables radiotherapy using stereotactic ablative body radiotherapy (SABR) with a large number of non-coplanar beam orientations. Recently, a multileaf collimator has also been available to allow flexibility in field shaping. This work aims to evaluate the quality of treatment plans obtainable with the multileaf collimator. Specifically, the aim is to find a subset of beam orientations from a predetermined set of candidate directions, such that the treatment quality is maintained but the treatment time is reduced. An evolutionary algorithm is used to successively refine a randomly selected starting set of beam orientations. By using an efficient computational framework, clinically useful solutions can be found in several hours. It is found that 15 beam orientations are able to provide treatment quality which approaches that of the candidate beam set of 110 beam orientations, but with approximately half of the estimated treatment time. Choice of an efficient subset of beam orientations offers the possibility to improve the patient experience and maximise the number of patients treated

Towards on-line plan adaptation of unified intensity-modulated arc therapy using a fast-direct aperture optimization algorithm

External beam radiotherapy (EBRT) plays a vital role in the treatment of cancer, with close to half of all cancer patients receiving EBRT at some point over their course of treatment. Although EBRT is a well-established form of treatment, there are a number of ways in which EBRT could still be improved in terms of quality and efficiency for treatment planning and radiation dose delivery. This thesis reports a series of improvements made to EBRT. First, we developed and evaluated a new treatment planning technique called unified intensity-modulated arc therapy (UIMAT) which combines the optimization and delivery of rotational volumetric modulated arc therapy (VMAT) and fixed-gantry intensity-modulated radiation therapy (IMRT). When retrospectively compared to clinical treatment plans using VMAT or IMRT alone, UIMAT plans reduced the dose to nearby critical structures by as much as 23% without compromising tumour volume coverage. The UIMAT plans were also more efficient to deliver. The reduction in normal tissue dose could help lower the probability of treatment-related toxicities, or alternatively could be used to improve tumour control probability, via dose escalation, while maintaining current dose limits for organs at risk. Second, we developed a new fast inverse direct aperture optimization (FIDAO) algorithm for IMRT, VMAT, and UIMAT treatment planning. FIDAO introduces modifications to the direct aperture optimization (DAO) process that help improve its computational efficiency. As demonstrated in several test cases, these modifications do not significantly impact the plan quality but reduced the DAO time by as much as 200-fold. If implemented with graphical processing units (GPUs), this project may allow for applications such as on-line treatment adaptation. Third, we investigated a method of acquiring tissue density information from cone-beam computed tomography (CBCT) datasets for on-line dose calculations, plan assessment, and potentially plan adaptation using FIDAO. This calibration technique accounts for patient-specific scattering conditions, demonstrated high dosimetric accuracy, and can be easily automated for on-line plan assessment. Collectively, these three projects will help reduce the normal tissue doses from EBRT, improve the planning and delivery efficiency, and pave the way for application like on-line plan assessment and adaptive radiotherapy in response to anatomical changes

DEVELOPMENT AND INVESTIGATION OF INTENSITY-MODULATED RADIATION THERAPY TREATMENT PLANNING FOR FOUR-DIMENSIONAL ANATOMY

Lung cancer is the leading cause of cancer-related deaths worldwide. Radiotherapy is one of the main treatment modalities of lung cancer. However, the achievable accuracy of radiotherapy treatment is limited for lung-based tumors due to respiratory motion. Four-dimensional radiotherapy explicitly accounts for anatomic motion by characterizing the motion, creating a treatment plan that accounts for this motion, and delivering this plan to the moving anatomy. This thesis focuses on the current problems and solutions throughout the course of four-dimensional radiotherapy. For characterization of respiratory-induced motion, patient tumor motion data were analyzed. It is shown that tumor motion can be significant during radiotherapy treatment, and its extent, direction, and linearity vary considerably between patients, between treatment fractions, and between respiratory cycles. After this, approaches to four-dimensional intensity-modulated radiation therapy treatment planning were developed and investigated. Among the techniques to manage respiratory motion, tumor tracking using a dynamic multileaf collimator delivery technique was chosen as a promising method. A formalism to solve a general four-dimensional intensity-modulated radiation therapy treatment-planning problem was developed. Specific solutions to this problem accounting for tumor motion initially in one dimension and extending this to three dimensions were developed and investigated using four-dimensional computed tomography planning scans of lung cancer patients. For four-dimensional radiotherapy treatment delivery, accuracy of two-dimensional projection imaging methods was investigated. Geometric uncertainty due to the limitation of two-dimensional imaging in monitoring three-dimensional tumor motion during treatment delivery was quantified. This geometric uncertainty can be used to estimate proper margins when a single two-dimensional projection imager is used for four-dimensional treatment delivery. Lastly, tumor-tracking delivery using a moving average algorithm was investigated as an alternative delivery technique that reduces mechanical motion constraints of a multileaf collimator. Moving average tracking provides an approximate solution that can be immediately implemented for delivery of four-dimensional intensity-modulated radiation therapy treatment. The clinical implementation of four-dimensional guidance, intensity-modulated radiation therapy treatment planning, and dynamic multileaf collimator tracking delivery may have a positive impact on the treatment of lung cancer