The matrix orthogonal decomposition problem in intensity-modulated radiation therapy

Authors:
Xin Dou;Xiaodong Wu;John E. Bayouth;John M. Buatti
Affiliations:
Dept. of Electrical and Computer Engineering, University of Iowa, Iowa City, Iowa;Dept. of Electrical and Computer Engineering, University of Iowa, Iowa City, Iowa;Dept. of Radiation Oncology, University of Iowa, Iowa City, Iowa;Dept. of Radiation Oncology, University of Iowa, Iowa City, Iowa
Venue:
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Year:
2006

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Abstract

In this paper, we study an interesting matrix decomposition problem that seeks to decompose a “complicated” matrix into two “simpler” matrices while minimizing the sum of the horizontal complexity of the first sub-matrix and the vertical complexity of the second sub-matrix. The matrix decomposition problem is crucial for improving the “step-and-shoot” delivery efficiency in Intensity-Modulated Radiation Therapy, which aims to deliver a highly conformal radiation dose to a target tumor while sparing the surrounding normal tissues. Our algorithm is based on a non-trivial graph construction scheme, which enables us to formulate the decomposition problem as computing a minimum s-t cut in a 3-D geometric multi-pillar graph. Experiments on randomly generated intensity map matrices and on clinical data demonstrated the efficiency of our algorithm.