Title: Optimization of Gamma Knife Radiosurgery

Abstract:

The Gamma Knife is a highly specialized treatment unit that provides an advanced stereotactic approach to the treatment of tumors, vascular malformations, and pain disorders within the head. Inside a shielded treatment unit, beams from 201 radioactive sources are focused so that they intersect at the same location in space, resulting in a spherical region of high dose referred to as a shot of radiation. The location and width of the shots can be adjusted using focusing helmets. By properly combining a set of shots, larger treatment volumes can be successfully treated with the Gamma Knife. It is therefore possible to automate the treatment planning process. For each patient, an optimization seeks to produce a dose distribution that conforms closely to the treatment volume. The variables in the optimization can include the number of shots of radiation along with the size, the location, and the weight assigned to each. Formulation of such problems using a variety of mathematical programming models is described, and the solution of several test and real-patient examples is demonstrated.

Title: Multicriteria Optimization in Radiation Therapy

Abstract:

Radiation therapy is one of the most frequently used tools in fighting cancer. Several mathematical optimization problems need to be solved to find for each patient the best possible therapy, include the following:

- At which angles should the radiation gantry stop (geometry or angle problem)?

- Which kind of intensity should be sent off at each of the angles to achieve a conformal radiation (intensity problem)?

- How should the radiation be implemented using multileaf collimators (MLC problem)?

All of these problems are at this point of time only partially solved. Since the evaluation of the decisions is in all of these cases dependent on more than one objective, it is obvious, that a multicriteria approach is useful in many instances. The mathematical challenge in this approach it that one is dealing with large scale problems and that a finite representative set of all Pareto optimal solutions is needed in order to help the radiation planner. In the talk, recent results in solving radiation problems in a multicriteria environment will be presented.

Title: Optimization in Epilepsy

Abstract:

Epileptic seizures are manifestations of intermittent spatio-temporal transitions of the human brain from chaos to order. These transitions can be quantified by measures from nonlinear dynamics, namely Lyapunov exponents and correlation integrals, estimated from the electrical activity (EEG) of the brain over time at electrode sites overlying the epileptogenic zone as well as normal brain areas. By analysis of the above nonlinear dynamical measures, it has been shown that the core of these transitions is the progressive entrainment of critical brain sites by the epileptogenic focus long prior to the occurrence of an epileptic seizure. The use of optimization techniques (i.e., quadratic integer programming) for the selection of the critical brain sites can lead to long-term prediction of impending epileptic seizures, as well as to the localization of the epileptogenic focus. Both issues are of tremendous clinical and scientific importance. The combination of techniques from nonlinear dynamics and optimization can be used for prediction of upcoming transitions in other complex biological and physical systems that undergo intermittent spatio-temporal transitions.

Title: Optimal Reconstruction Kernels in Medical Imaging

Abstract:

In medical imaging like x-ray tomography or MRI the searched-for information has to be recovered from the measured data. Nowadays typically one reconstructs the object, either in two or three dimensions and displays the images on a screen. The evaluation is completely left to the physician. We present a technology to derive reconstruction algorithms for different imaging technologies like 3D cone beam tomography and EPRI. To speed up the computation special features of the data assembling are used. Furthermore we consider the fact that for analyzing the images only moments of them are sometimes used. We present optimal strategies for their reconstruction. Real data applications in 3D x-ray CT are presented.

Title: Optimization and Optimal Control in High Intensity Ultrasound Surgery

Abstract:

High intensity focused ultrasound (HIFU) has been long planned to be used in treating tumors. This is to be distinguished from hyperthermia, in which the tissue is moderately heated to enhance the effect of radiotherapy. In HIFU the tissue is heated to 60 - 95 degrees so that the thermal dose produces a lesion. The treatment is carried out by placing from tens to hundreds of ultrasound transducers around the relevant part of the patient boundary. Then the phases and the amplitudes of the transducers are controlled in such a fashion that ideally only the tumor is destroyed while the healthy tissue is not harmed. The associated optimization problem for temporal transducer evolutions under a number of constraints is heavily nonlinear and involves thousands of unknowns. We treat both the feedforward optimization problem as well as the feedback problem with magnetic resonance imaging based state observations.

Title: Integer Programming in Radiation Therapy

Abstract:

In recent years, technical advances in medical devices have led to improved delivery of radiation therapy treatment to cancer patients. These advances call for a renewed emphasis on developing sophisticated methods for designing treatment plans. In this talk, we will give an overview of the issues involved in treatment planning, and describe the use of sophisticated mathematical models and algorithms that have been demonstrated to be effective for treatment planning.

Brachytherapy is a radiation treatment that involves the placement of encapsulated radionuclides ("seeds") within or near a tumor. We will illustrate the use of mixed integer programming (MIP) in designing clinically relevant brachytherapy treatment plans, and demonstrate the challenges in the solution process. We also will highlight how tumor shrinkage and movement can be managed efficiently in the planning process.

In contrast to brachytherapy, external beam radiotherapy involves the use of radiation beams that traverse from a source external to the body, through healthy tissue, to access the tumor site. An advanced form of external beam radiation therapy, known as intensity-modulated radiotherapy (IMRT), allows each radiation beam to be subdivided into tiny "beamlets". This enables a high degree of variation/modulation of the intensity within each beam. Appropriate use of IMRT has the potential to lead to substantially better treatment than was previously possible. However, the high level of variation leads to challenging issues in treatment planning. We will describe large-scale MIP models for IMRT treatment planning designed to find the "optimal" configuration of beam angles and beamlet intensities so as to deliver a necrotic dose of radiation to the tumor itself, while limiting radiation to healthy tissue.

Title: Optimization in Medical Imaging Registration

Abstract:

Registration refers to the process of aligning two or more images with minimum shape difference being the alignment criterion. In medical imaging, the problem of registering multiple images frequently arises. Since the images can be acquired from different modalities (PET, fMRI) or from different subjects, the task of medical image registration can be quite challenging. Due to the natural shape differences that are manifest across subjects, inter-subject image registration forces us to use non-rigid alignment criteria. In our formulation of this problem, we first select a set of shape features resulting in two sets of features, one from each image. Then we try to find the smallest shape deformation that can approximately take one set of shape features onto the other. If we knew the counterpart in set two of each shape feature in set one, the estimation of the minimum shape difference would be reasonably straightforward. Since this information is unknown a priori, we attempt to discover the feature counterparts while minimizing the shape difference. The result is an integrated optimization algorithm which simultaneously estimates the feature counterparts and the shape deformation that lead to best alignment. We demonstrate the application of this algorithm in a variety of domains including the rigid alignment of primate autoradiographs and the non-rigid registration of cortical anatomical structures as seen in MRI.