Improved Approximation Algorithms for Segment Minimization in Intensity Modulated Radiation Therapy

he segment minimization problem consists of finding the smallest set of integer matrices that sum to a given intensity matrix, such that each summand has only one non-zero value, and the non-zeroes in each row are consecutive. This has direct applications in intensity-modulated radiation therapy, an effective form of cancer treatment. We develop three approximation algorithms for matrices with arbitrarily many rows. Our first two algorithms improve the approximation factor from the previous best of $1+\log_2 h$ to (roughly) $3/2 \cdot (1+\log_3 h)$ and $11/6\cdot(1+\log_4{h})$, respectively, where $h$ is the largest entry in the intensity matrix. We illustrate the limitations of the specific approach used to obtain these two algorithms by proving a lower bound of $\frac{(2b-2)}{b}\cdot\log_b{h} + \frac{1}{b}$ on the approximation guarantee. Our third algorithm improves the approximation factor from $2 \cdot (\log D+1)$ to $24/13 \cdot (\log D+1)$, where $D$ is (roughly) the largest difference between consecutive elements of a row of the intensity matrix. Finally, experimentation with these algorithms shows that they perform well with respect to the optimum and outperform other approximation algorithms on 77% of the 122 test cases we consider, which include both real world and synthetic data.Comment: 18 page

The Possibilities and Dosimetric Limitations of MLC-Based Intensity-Modulated Radiotherapy Delivery and Optimization Techniques

The use of intensity-modulated radiotherapy (IMRT) has increased extensively in the modern radiotherapy (RT) treatments over the past two decades. Radiation dose distributions can be delivered with higher conformality with IMRT when compared to the conventional 3D-conformal radiotherapy (3D-CRT). Higher conformality and target coverage increases the probability of tumour control and decreases the normal tissue complications. The primary goal of this work is to improve and evaluate the accuracy, efficiency and delivery techniques of RT treatments by using IMRT. This study evaluated the dosimetric limitations and possibilities of IMRT in small (treatments of head-and-neck, prostate and lung cancer) and large volumes (primitive neuroectodermal tumours). The dose coverage of target volumes and the sparing of critical organs were increased with IMRT when compared to 3D-CRT. The developed split field IMRT technique was found to be safe and accurate method in craniospinal irradiations. By using IMRT in simultaneous integrated boosting of biologically defined target volumes of localized prostate cancer high doses were achievable with only small increase in the treatment complexity. Biological plan optimization increased the probability of uncomplicated control on average by 28% when compared to standard IMRT delivery. Unfortunately IMRT carries also some drawbacks. In IMRT the beam modulation is realized by splitting a large radiation field to small apertures. The smaller the beam apertures are the larger the rebuild-up and rebuild-down effects are at the tissue interfaces. The limitations to use IMRT with small apertures in the treatments of small lung tumours were investigated with dosimetric film measurements. The results confirmed that the peripheral doses of the small lung tumours were decreased as the effective field size was decreased. The studied calculation algorithms were not able to model the dose deficiency of the tumours accurately. The use of small sliding window apertures of 2 mm and 4 mm decreased the tumour peripheral dose by 6% when compared to 3D-CRT treatment plan. A direct aperture based optimization (DABO) technique was examined as a solution to decrease the treatment complexity. The DABO IMRT technique was able to achieve treatment plans equivalent with the conventional IMRT fluence based optimization techniques in the concave head-and-neck target volumes. With DABO the effective field sizes were increased and the number of MUs was reduced with a factor of two. The optimality of a treatment plan and the therapeutic ratio can be further enhanced by using dose painting based on regional radiosensitivities imaged with functional imaging methods.Siirretty Doriast

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

A Hierachical Evolutionary Algorithm for Multiobjective Optimization in IMRT

Purpose: Current inverse planning methods for IMRT are limited because they are not designed to explore the trade-offs between the competing objectives between the tumor and normal tissues. Our goal was to develop an efficient multiobjective optimization algorithm that was flexible enough to handle any form of objective function and that resulted in a set of Pareto optimal plans. Methods: We developed a hierarchical evolutionary multiobjective algorithm designed to quickly generate a diverse Pareto optimal set of IMRT plans that meet all clinical constraints and reflect the trade-offs in the plans. The top level of the hierarchical algorithm is a multiobjective evolutionary algorithm (MOEA). The genes of the individuals generated in the MOEA are the parameters that define the penalty function minimized during an accelerated deterministic IMRT optimization that represents the bottom level of the hierarchy. The MOEA incorporates clinical criteria to restrict the search space through protocol objectives and then uses Pareto optimality among the fitness objectives to select individuals. Results: Acceleration techniques implemented on both levels of the hierarchical algorithm resulted in short, practical runtimes for optimizations. The MOEA improvements were evaluated for example prostate cases with one target and two OARs. The modified MOEA dominated 11.3% of plans using a standard genetic algorithm package. By implementing domination advantage and protocol objectives, small diverse populations of clinically acceptable plans that were only dominated 0.2% by the Pareto front could be generated in a fraction of an hour. Conclusions: Our MOEA produces a diverse Pareto optimal set of plans that meet all dosimetric protocol criteria in a feasible amount of time. It optimizes not only beamlet intensities but also objective function parameters on a patient-specific basis

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

Controlling Beam Complexity in Intensity Modulated Radiation Therapy.

External beam intensity modulated radiation therapy (IMRT) is a technique in which the spatial intensity of radiation from each beam direction can be modulated to provide superior conformality of dose to a tumor volume while sparing important normal tissues. A fundamental and potentially limiting feature of IMRT is the highly complex fields that can be created through inverse plan optimization. Highly modulated treatments are a large departure from conventional radiotherapy methods, are difficult to deliver accurately and efficiently, and can result in an undesirable increase in leakage dose being delivered to the patient. Longer deliveries may also increase the chance for patient motion during treatment and could potentially reduce the probability of controlling some tumors. The large intensity fluctuations observed in IMRT beams are often a result of the degeneracy of the optimization problem, and the types of optimization method and cost function used. This work demonstrates that beam complexity is a result of these two issues, and is dependent on the placement of dose evaluation points in the target and normal tissues. This research shows that (i) optimizing surfaces instead of discrete beamlet intensities to represent the beam can reduce the degrees of freedom in IMRT and results in much smoother beams at the expense of a slight increase in normal tissues, (ii) maximum beamlet intensity restrictions are useful for improved delivery efficiency, but may restrict the optimizer at low limits, and (iii) modulation penalties can be incorporated into the cost function to promote plan smoothness without sacrificing plan quality. Penalizing the overall plan modulation is an effective way to reduce modulation, but it falsely penalizes the desirable beam modulation as well as the undesirable modulation. To address this problem, diffusion principles are used to develop a spatially adaptive smoothing method that only penalizes the unnecessary beam modulation and can be used without degrading plan quality. This method is customizable to a variety of treatment scenarios. The clinical impact of reducing beam complexity is significant, as it can result in an improvement in delivery accuracy and efficiency, quicker optimization times, and increased robustness to point sampling and geometric uncertainty.Ph.D.Nuclear Engineering & Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/57648/2/mcoselmo_1.pd

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