Hernán G. Abeledo

Needle-Based Interventions With the Image-Guided Surgery Toolkit (IGSTK): From Phantoms to Clinical Trials

We present three image-guided navigation systems developed for needle-based interventional radiology procedures, using the open source image-guided surgery toolkit (IGSTK). The clinical procedures we address are vertebroplasty, RF ablation of large lung tumors, and lung biopsy. In vertebroplasty, our system replaces the use of fluoroscopy, reducing radiation exposure to patient and physician. We evaluate this system using a custom phantom and compare the results obtained by a medical student, an interventional radiology fellow, and an attending physician. In RF ablation of large lung tumors, our system provides an automated interventional plan that minimizes damage to healthy tissue and avoids critical structures, in addition to accurate guidance of multiple electrode insertions. We evaluate the systems performance using an animal model. Finally, in the lung biopsy procedure, our system replaces the use of computed tomographic (CT) fluoroscopy, reducing radiation exposure to patient and physician, while at the same time enabling oblique trajectories which are considered challenging under CT fluoroscopy. This system is currently being used in an ongoing clinical trial at Georgetown University Hospital and was used in three cases.

The time dependent traveling salesman problem: polyhedra and algorithm

The time dependent traveling salesman problem (TDTSP) is a generalization of the classical traveling salesman problem (TSP), where arc costs depend on their position in the tour with respect to the source node. While TSP instances with thousands of vertices can be solved routinely, there are very challenging TDTSP instances with less than 100 vertices. In this work, we study the polytope associated to the TDTSP formulation by Picard and Queyranne, which can be viewed as an extended formulation of the TSP. We determine the dimension of the TDTSP polytope and identify several families of facet-defining cuts. We obtain good computational results with a branch-cut-and-price algorithm using the new cuts, solving almost all instances from the TSPLIB with up to 107 vertices.

Treatment Planning and Image Guidance for Radiofrequency Ablation of Large Tumors

This article addresses the two key challenges in computer-assisted percutaneous tumor ablation: planning multiple overlapping ablations for large tumors while avoiding critical structures, and executing the prescribed plan. Toward semiautomatic treatment planning for image-guided surgical interventions, we develop a systematic approach to the needle-based ablation placement task, ranging from preoperative planning algorithms to an intraoperative execution platform. The planning system incorporates clinical constraints on ablations and trajectories using a multiple objective optimization formulation, which consists of optimal path selection and ablation coverage optimization based on integer programming. The system implementation is presented and validated in both phantom and animal studies. The presented system can potentially be further extended for other ablation techniques such as cryotherapy.

Optimizing Helicopter Transport of Oil Rig Crews at Petrobras

Petrobras produces nearly 90 percent of Brazils oil at about 80 offshore oil platforms. It transports approximately 1,900 employees daily between these platforms and four mainland bases, using more than 40 helicopters that vary in capacity, operating costs, and performance characteristics. Each day, flight planners must select the helicopter routes and schedules that satisfy passenger demands. We developed a system that requires less than one hour to generate optimized flight plans that meet operational guidelines, improve travel safety, and minimize operating costs. By using this system, Petrobras reduced its number of offshore landings by 18 percent, total flight time by 8 percent, and flight costs by 14 percent, resulting in annual savings of more than

Radiofrequency ablation of lung tumors in swine assisted by a navigation device with preprocedural volumetric planning.

20 million. Our optimization model is a large-scale mixed integer program that generalizes prior helicopter routing models. We designed a column-generation algorithm that exploits the problem structure to overcome its computational difficulties. As part of the solution method, we use a network flow model to optimally assign passengers to selected routes.

A simulation-based approach to trade-off analysis of port security

PURPOSE To develop an image guidance system that incorporates volumetric planning of spherical ablations and electromagnetic tracking of radiofrequency (RF) electrodes during insertion. MATERIALS AND METHODS Simulated tumors were created in three live swine by percutaneously injecting agar nodules into the lung. A treatment plan was devised for each tumor with optimization software to solve the planning problem. The desired output was the minimum number of overlapping ablation spheres necessary to ablate each tumor and the margin. The insertion plan was executed with use of the electromagnetic tracking system that guided the insertion of the probe into precomputed locations. After a 72-hour survival period, animals were killed and histopathologic sections of the tissue were examined for cell viability and burn pattern analysis. RESULTS A planning algorithm to spherically cover the tumors and the margin was computed. Electromagnetic tracking allowed successful insertion of the instrument, and impedance roll-off was reached in all ablations. Depending on their size, the tumors and the tumor margins were successfully covered with two to four ablation spheres. The image registration error was 1.0 mm +/- 0.64. The overall error of probe insertion was 9.4 mm +/- 3.0 (N = 8). Analysis of histopathologic sections confirmed successful ablations of the tissue. CONCLUSIONS Computer-assisted RF ablation planning and electromagnetically tracked probe insertion were successful in three swine, validating the feasibility of electromagnetic tracking-assisted tumor targeting. Image misregistration caused by respiratory motion and tissue deformation contributed to the overall error of probe insertion.

The time dependent traveling salesman problem: polyhedra and branch-cut-and-price algorithm

Motivated by the September 11 attacks, we are addressing the problem of policy analysis of supply-chain security. Considering the potential economic and operational impacts of inspection together with the inherent difficulty of assigning a reasonable cost to an inspection failure call for a policy analysis methodology in which stakeholders can understand the trade-offs between the diverse and potentially conflicting objectives. To obtain this information, we used a simulation-based methodology to characterize the set of Pareto optimal solutions with respect to the multiple objectives represented in the decision problem. Our methodology relies on simulation and the response surface method (RSM) to model the relationships between inspection policies and relevant stakeholder objectives in order to construct a set of Pareto optimal solutions. The approach is illustrated with an application to a real-world supply chain

Stable matchings and linear programming

The Time Dependent Traveling Salesman Problem (TDTSP) is a generalization of the classical Traveling Salesman Problem (TSP), where arc costs depend on their position in the tour with respect to the source node. While TSP instances with thousands of vertices can be solved routinely, there are very challenging TDTSP instances with less than 60 vertices. In this work, we study the polytope associated to the TDTSP formulation by Picard and Queyranne, which can be viewed as an extended formulation of the TSP. We determine the dimension of the TDTSP polytope and identify several families of facet defining cuts. In particular, we also show that some facet defining cuts for the usual Asymmetric TSP formulation define low dimensional faces of the TDTSP formulation and give a way to lift them. We obtain good computational results with a branch-cut-and-price algorithm using the new cuts, solving several instances of reasonable size at the root node.

Canonical monotone decompositions of fractional stable matchings

Abstract This paper continues the work of Abeledo and Rothblum, who study nonbipartite stable matching problems from a polyhedral perspective. We establish here additional properties of fractional stable matchings and use linear programming to obtain an alternative polynomial algorithm for solving stable matching problems.

A min-max theorem for plane bipartite graphs

This paper continues recent work that introduced algebraic methods for studying the stable marriage problem of Gale and Shapley [1962]. Vande Vate [1989] and Rothblum [1992] identified a set of linear inequalities which define a polytope whose extreme points correspond to the stable matchings. Points in this polytope are called fractional stable matchings. Here we identify a unique representation of fractional stable matchings as a convex combination of stable matchings that are arrangeable in a man-decreasing order. We refer to this representation and to a dual one, in terms of woman-decreasing order, as the canonical monotone representations. These representations can be interpreted as time-sharing stable matchings where particular stable matchings are used at each time-instance but the scheduled stable matchings are (occasionally) switched over time. The new representations allow us to extend, in a natural way, the lattice structure of the set of stable matchings to the set of all fractional stable matchings.