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  • A Fully-Automated

    Intensity-Modulated Radiation Therapy

    Planning System

    Shabbir Ahmed, Ozan Gozbasi, Martin Savelsbergh

    Georgia Institute of Technology

    Ian Crocker, Tim Fox, Eduard Schreibmann

    Emory University

    Abstract

    We designed and implemented a linear programming based IMRT treatment plan generation

    technology that effectively and efficiently optimizes beam geometry as well as beam intensities.

    The core of the technology is a fluence map optimization model that approximates partial dose

    volume constraints using conditional value-at-risk constraints. Conditional value-at-risk con-

    straints require careful tuning of their parameters to achieve desirable plan quality and therefore

    we developed an automated search strategy for parameter tuning. Another novel feature of our

    fluence map optimization model is the use of virtual critical structures to control coverage and

    conformity. Finally, beam angle selection has been integrated with fluence map optimization.

    The beam angle selection scheme employs a bi-criteria weighting of beam angle geometries and

    a selection mechanism to choose from among the set of non-dominated geometries. The tech-

    nology is fully automated and generates several high-quality treatment plans satisfying dose

    prescription requirements in a single invocation and without human guidance. The technology

    has been tested on various real patient cases with uniform success. Solution times are an order

    of magnitude faster than what is possible with currently available commercial planning systems

    and the quality of the generated treatment plans is at least as good as the quality of the plans

    produced with existing technology.

    1 Introduction

    External beam irradiation is used to treat over 500,000 cancer patients annually in the United

    States. External beam radiation therapy uses multiple beams of radiation from different directions

    to cross-fire at a cancerous tumor volume. Thus, radiation exposure of normal tissue is kept at

    low levels, while the desired dose to the tumor volume is delivered. The key to the effectiveness

    of radiation therapy for the treatment of cancer lies in the fact that the repair mechanisms for

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  • cancerous cells are less efficient than those of normal cells. Intensity-modulated radiation therapy

    (IMRT) is a relatively recent advance in treatment delivery in radiation therapy. In IMRT, the

    beam intensity is varied across each treatment field. Rather than being treated with a large uniform

    beam, the patient is treated instead with many small pencil beams (referred to as beamlets), each

    of which can have a different intensity. For many types of cancer, such as prostate cancer and

    head and neck cancer, the use of intensity modulation allows more concentrated treatment of the

    tumor volume, while limiting the radiation dose to adjacent healthy tissue (see Veldeman et al. [20]

    for comparisons of IMRT and non-IMRT treatments on different tumor sites). IMRT treatment

    planning is concerned with selecting a beam geometry and beamlet intensities to produce the best

    dose distribution. Because of the many possible beam geometries, the large number of beamlets, and

    the range of beamlet intensities, there is an infinite number of treatment plans, and consistently and

    efficiently generating high-quality treatment plans is beyond human capability. Consequently, it is

    necessary to design and implement optimization-based decision support systems that can construct

    and suggest high-quality treatment plans in a short period of time. That is the goal of our research

    and the subject of this paper.

    Constructing an IMRT treatment plan that radiates the cancerous tumor volume without im-

    pacting normal structures is virtually impossible. Therefore, trade-offs have to be made. Radiation

    oncologists have developed a variety of measures to evaluate these trade-offs and to assess the

    quality of a treatment plan, such as the coverage of a target volume by a prescription dose, the

    conformity of a prescription dose around a target volume, the highest and the lowest doses received

    by a target volume. Furthermore, radiation oncologists review dose-volume histograms (DVHs)

    depicting the dose distributions at various structures (both target volumes and organs at risk) of

    treatment plans. Typically, a radiation oncologist specifies a set of dose-related minimum require-

    ments (a set of prescriptions) that have to be satisfied in any acceptable treatment plan. The

    measures and DVHs are then used to choose among acceptable treatment plans. Further com-

    plicating the evaluation of treatment plans is the fact that the minimum requirements and their

    relative importance are subjective as are the underlying trade-offs they are trying to capture. As

    a result, most existing IMRT treatment planning systems are iterative in nature and necessitate

    human evaluation and guidance throughout the treatment plan construction process. This makes

    the process time-consuming and costly. One of the primary goals of our research is the develop-

    ment of fully-automated treatment plan generation technology that completely eliminates human

    intervention, thereby saving valuable time for the radiation oncologist and physicist.

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  • Natural models of dose-volume requirements result in nonlinear and/or mixed integer programs,

    which are notoriously hard to solve. Recently, Romeijn et al. ([18]) observed that conditional

    value-at-risk constraints (C-VaR constraints), which are popular and commonly used in financial

    engineering, can be used to approximate dose-volume constraints. The use of C-VaR constraints

    has significant computational advantages as they can be handled using linear programming models,

    which are easily and efficiently solved. However, the parameters controlling the C-VaR constraints

    have to be chosen carefully to get an accurate approximation of the dose-volume constraints. Our

    treatment plan generation technology, which is based on an optimization model using C-VaR con-

    straints, embeds an effective and efficient parameter search scheme to ensure high-quality approx-

    imations of the dose-volume constraints. Another innovation in our treatment plan generation

    technology is the use of virtual critical structures. Virtual critical structures surround target vol-

    umes and are implemented to control the dose deposits specifically at the boundary of the target

    volume.

    Our treatment plan generation technology incorporates an effective and efficient scheme for

    the selection of beam geometries, which is ignored in many commercial planning systems as it

    adds another layer of complexity to the search for high-quality treatment plans. Most commercial

    planning systems consider only beam geometries involving a small number of equi-distant beam

    angles around a circle (on the order of 5 to 8). Because of the computational efficiency of our core

    plan generation technology, we are able to embed a scheme that optimizes the beam geometry. At

    the heart of the scheme is a multi-attribute beam scoring mechanism based on a treatment plan

    constructed for a beam geometry involving a large number of beam angles (on the order of to 24).

    In summary, we have developed treatment plan generation technology that optimizes both beam

    geometry and beamlet intensities in a short amount of time. The technology is fully automated

    and generates several high-quality treatment plans satisfying the provided minimum requirements

    in a single invocation and without human guidance. The technology has been tested on various real

    patient cases with great success. Solution times range from a few minutes to a quarter of an hour,

    which is an order of magnitude faster than what is possible with currently available commercial

    planning systems. Furthermore, the quality of the generated treatment plans is at least as good as

    those produced with existing technology.

    The remainder of the paper is organized as follows. In Section 2, we introduce IMRT treatment

    plan generation and evaluation in more detail. In Section 3, we describe the core components of

    the IMRT treatment plan generation technology that we have developed. Finally, in Section 4, we

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  • present the results of an extensive computational study.

    2 Problem Description

    Intensity-modulated radiation therapy (IMRT) is an advanced mode of high-precision radiotherapy

    that utilizes computer-controlled mega-voltage x-ray accelerators to deliver precise radiation doses

    to a cancerous tumor or specific areas within the tumor. The radiation dose is designed to conform

    to the three-dimensional (3-D) shape of the tumor by modulating – or controlling - the intensity of

    the radiation beam to focus a higher radiation dose to the tumor while minimizing radiation expo-

    sure to surrounding normal tissues. Typically, combinations of several intensity-modulated fields

    coming from different beam directions produce a custom tailored radiation dose that maximizes

    tumor dose while also protecting adjacent normal tissues. IMRT is being used to treat cancers of

    the prostate, head and neck, breast, thyroid, lung, liver, brain tumors, lymphomas and sar

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