July 30-August 2, 2008
Society for Mathematical Biology Conference

hosted by the Centre for Mathematical Medicine, Fields Institute
held at University of Toronto, Medical Sciences Bldg


Back to mini-symposia index

12) Minimizing the adverse effects of uncertainities in external radiation therapy
Principal organiser: Dr. Yuriy Zinchenko
Advanced Optimization Laboratory, McMaster University & Department of Radiation Oncology, Princess Margaret Hospital, CAS, McMaster University
& Department of Mathematics, University of Calgary

Motion-induced and structural uncertainties in radiation therapy severely limit the efficacy of the treatment. We target minimizing adverse effects of uncertainties in IMRT during the treatment planning using a combination of image guidance and novel large-scale robust optimization techniques, pioneered by our group 5 years ago.
Robust optimization allows exploiting not only spatial, but also temporal characteristics of the uncertainties, in order to produce more aggressive treatment plans. Computational studies indicate superiority of this approach over the traditional treatment planning, however, further investigation is required.
The minisymposium is intended for radiation physicists, oncologists, treatment planning software developers and applied mathematicians.

1. Laura Dawson, Department of Radiation Oncology, Princess Margaret Hospital
High-precision radiotherapy for hepatobiliary cancer: the effects of uncertainties.

The projected increase in the incidence and mortality of thoracic and abdominal cancers is an important health concern for Canadians. For many diseases, radiation therapy is a proven treatment modality, and nearly half of all cancer patients receive radiation therapy, either as the sole treatment modality or in combination with surgery and/or systemic pharmaceutical agents, e.g. chemotherapy. Important technological advances, such as intensity modulated radiation therapy (IMRT), have solidified or expanded the role of radiation therapy in improving control of cancers and reducing toxicity, notably for head and neck cancers and prostate cancer. For disease in the thorax and abdomen, however, the effectiveness of radiotherapy has been limited by the sensitivity of non-tumorous lung and liver tissues, and confounded by the technical challenges associated with breathing-related organ movement and patient setup uncertainty. Highly tailored treatments, where the high dose volume matches the shape and position of the cancer, minimize the dose to healthy tissue but also create the risk of a geometric miss of the disease. Without effective targeting there is a risk of damaging healthy tissues indiscriminately and failing to control the disease, even using IMRT technologies. We believe there is a compelling need to develop properly targeted IMRT in order to yield significant gains in the control of lung and liver cancer, including cancer originating in the lung and liver, as well as metastases to these sites from colorectal cancer and breast cancer.
We discuss how the uncertainties impact the efficacy of the radiation treatment for primary and secondary liver cancers – a particularly challenging site for this type of treatment modality.

2. Tamás Terlaky, School of Computational Engineering and Science, McMaster University
Large-scale convex and robust optimization: introduction and applications

Two decades of Interior Point Method research opened new avenues to solve large scale optimization problems. Novel modeling methodologies, such as convex conic and robust optimization were developed. Now we are able to model and routinely solve large-scale problems with high practical importance. In this talk we review the state-of-art of large scale convex optimization, discuss the Ben Tal - Nemirovski robust optimization model, review some novel applications and illustrate the power of the state-of-the art SeDuMi conic linear optimization software package.

3. Kristy Brock, Department of Radiation Oncology, Princess Margaret Hospital
Novel deformable image registration techniques to facilitate classification, targeting, and monitoring of tumor and normal tissue response using finite element modeling.

As more pretreatment imaging becomes integrated into the treatment planning process and full three-dimensional image-guidance becomes part of the treatment delivery the need for a deformable image registration technique becomes more apparent. Several novel finite element model-based multi-organ deformable image registration methods, e.g., MORFEUS, have been developed. A common basis of these methods is twofold: first, individual organ deformation can be accurately modeled by deforming the surface of the organ at one instance into the surface of the organ at another instance and assigning the material properties that allow the internal structures to be accurately deformed into the secondary position and second, multi-organ deformable alignment can be achieved by explicitly defining the deformation of a subset of organs and assigning surface interfaces between organs. The feasibility and accuracy of the method was tested in a clinical setting. We discuss the potential applicability of these models.

4. Yuriy Zinchenko, Department of Mathematics, University of Calgary
Convex and robust optimization for IMRT treatment planning

Our goal is to develop treatment planning strategies that combine the assessment and intervention capabilities of IGRT with novel robust and adaptive large-scale optimization techniques to maximize the use of available patient information while limiting the need for real-time corrective intervention. The process of IMRT treatment planning, besides acquiring the initial medical imaging data and setting proper clinical objectives, typically involves formulating and solving an inverse problem that models treatment delivery. Optimization techniques are used commonly for the inverse problem, in order to attain the treatment delivery that is the best possible fit to specified clinical objectives.
To reduce the computational burden associated with IMRT treatment planning, we propose a convex optimization model that incorporates the desired dose distribution requirements. To minimize the negative effects of the uncertainties, we propose a convex robust model, which is partially based on probabilistic reading of the constraints. Both models fall within the framework of structured convex optimization, and, thus, are potentially amenable to Interior Point Methods. We highlight current challenges associated with both of the approaches


Back to