scholarly journals Discrete approximations to real-valued leaf sequencing problems in radiation therapy

2008 ◽  
Vol 156 (17) ◽  
pp. 3178-3186 ◽  
Author(s):  
Athula Gunawardena ◽  
Robert R. Meyer
Keyword(s):  
Radiation Therapy ◽  
Discrete Approximations ◽  
Leaf Sequencing ◽  
Sequencing Problems

GENERALIZED GEOMETRIC APPROACHES FOR LEAF SEQUENCING PROBLEMS IN RADIATION THERAPY

2006 ◽  
Vol 16 (02n03) ◽  
pp. 175-204 ◽  
Author(s):  
DANNY Z. CHEN ◽  
XIAOBO X. HU ◽  
SHUANG LUAN ◽  
SHAHID A. NAQVI ◽  
CHAO WANG ◽  
...  
Keyword(s):  
Radiation Therapy ◽  
Error Bound ◽  
Error Control ◽  
Medical Literature ◽  
Treatment Time ◽  
Treatment Plan ◽  
Minimum Cost ◽  
Leaf Sequencing ◽  
Sequencing Problems ◽  
Minimum Cost Flows

The 3-D static leaf sequencing (SLS) problem arises in radiation therapy for cancer treatments, aiming to deliver a prescribed radiation dose to a target tumor accurately and efficiently. The treatment time and machine delivery error are two crucial factors to the solution (i.e., a treatment plan) for the SLS problem. In this paper, we prove that the 3-D SLS problem is NP-hard, and present the first ever algorithm for the 3-D SLS problem that can determine a tradeoff between the treatment time and machine delivery error (also called the "tongue-and-groove" error in medical literature). Our new 3-D SLS algorithm with error control gives the users (e.g., physicians) the option of specifying a machine delivery error bound, and subject to the given error bound, the algorithm computes a treatment plan with the minimum treatment time. We formulate the SLS problem with error control as computing a k-weight shortest path in a directed graph and build the graph by computing g-matchings and minimum cost flows. Further, we extend our 3-D SLS algorithm to all the popular radiotherapy machine models with different constraints. In our extensions, we model the SLS problems for some of the radiotherapy systems as computing a minimum g-path cover of a directed acyclic graph. We implemented our new 3-D SLS algorithm suite and conducted an extensive comparison study with commercial planning systems and well-known algorithms in medical literature. Some of our experimental results based on real medical data are presented.

Generalized Geometric Approaches for Leaf Sequencing Problems in Radiation Therapy

2004 ◽  
pp. 271-281 ◽  
Author(s):  
Danny Z. Chen ◽  
Xiaobo S. Hu ◽  
Shuang Luan ◽  
Shahid A. Naqvi ◽  
Chao Wang ◽  
...  
Keyword(s):  
Radiation Therapy ◽  
Leaf Sequencing ◽  
Sequencing Problems

Generalized Geometric Approaches for Leaf Sequencing Problems in Radiation Therapy,

2005 ◽  
pp. 1176-1186
Author(s):  
Danny Z. Chen ◽  
Xiaobo S. Hu ◽  
Shuang Luan ◽  
Shahid A. Naqvi ◽  
Chao Wang ◽  
...  
Keyword(s):  
Radiation Therapy ◽  
Leaf Sequencing ◽  
Sequencing Problems

GEOMETRIC ALGORITHMS FOR STATIC LEAF SEQUENCING PROBLEMS IN RADIATION THERAPY

2004 ◽  
Vol 14 (04n05) ◽  
pp. 311-339 ◽  
Author(s):  
DANNY Z. CHEN ◽  
XIAOBO S. HU ◽  
SHUANG (SEAN) LUAN ◽  
CHAO WANG ◽  
XIAODONG WU
Keyword(s):  
Radiation Therapy ◽  
Polynomial Time ◽  
Geometric Algorithms ◽  
Planning System ◽  
Treatment Planning System ◽  
Polygonal Domain ◽  
Steiner Points ◽  
Delivery Times ◽  
Leaf Sequencing ◽  
Monotone Polygons

The static leaf sequencing (SLS) problem arises in radiation therapy for cancer treatments, aiming to accomplish the delivery of a radiation prescription to a target tumor in the minimum amount of delivery time. Geometrically, the SLS problem can be formulated as a 3-D partition problem for which the 2-D problem of partitioning a polygonal domain (possibly with holes) into a minimum set of monotone polygons is a special case. In this paper, we present new geometric algorithms for a basic case of the 3-D SLS problem (which is also of clinical value) and for the general 3-D SLS problem. Our basic 3-D SLS algorithm, based on new geometric observations, produces guaranteed optimal quality solutions using O(1) Steiner points in polynomial time; the previously best known basic 3-D SLS algorithm gives optimal outputs only for the case without considering any Steiner points, and its time bound involves a multiplicative factor of a factorial function of the input. Our general 3-D SLS algorithm is based on our basic 3-D SLS algorithm and a polynomial time algorithm for partitioning a polygonal domain (possibly with holes) into a minimum set of x-monotone polygons, and has a fast running time. Experiments of our SLS algorithms and software in clinical settings have shown substantial improvements over the current most popular commercial treatment planning system and the most well-known SLS algorithm in medical literature. The radiotherapy plans produced by our software not only take significantly shorter delivery times, but also have a much better treatment quality. This proves the feasibility of our software and has led to its clinical applications at the Department of Radiation Oncology at the University of Maryland Medical Center. Some of our techniques and geometric procedures (e.g., for partitioning a polygonal domain into a minimum set of x-monotone polygons) are interesting in their own right.

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