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Proceedings Paper

Sensitivity analysis of Jacobian determinant used in treatment planning for lung cancer
Author(s): Wei Shao; Sarah E. Gerard; Yue Pan; Taylor J. Patton; Joseph M. Reinhardt; Oguz C. Durumeric; John E. Bayouth; Gary E. Christensen
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Paper Abstract

Four-dimensional computed tomography (4DCT) is regularly used to visualize tumor motion in radiation therapy for lung cancer. These 4DCT images can be analyzed to estimate local ventilation by finding a dense correspondence map between the end inhalation and the end exhalation CT image volumes using deformable image registration. Lung regions with ventilation values above a threshold are labeled as regions of high pulmonary function and are avoided when possible in the radiation plan. This paper investigates a sensitivity analysis of the relative Jacobian error to small registration errors. We present a linear approximation of the relative Jacobian error. Next, we give a formula for the sensitivity of the relative Jacobian error with respect to the Jacobian of perturbation displacement field. Preliminary sensitivity analysis results are presented using 4DCT scans from 10 individuals. For each subject, we generated 6400 random smooth biologically plausible perturbation vector fields using a cubic B-spline model. We showed that the correlation between the Jacobian determinant and the Frobenius norm of the sensitivity matrix is close to -1, which implies that the relative Jacobian error in high-functional regions is less sensitive to noise. We also showed that small displacement errors on the average of 0.53 mm may lead to a 10% relative change in Jacobian determinant. We finally showed that the average relative Jacobian error and the sensitivity of the system for all subjects are positively correlated (close to +1), i.e. regions with high sensitivity has more error in Jacobian determinant on average.

Paper Details

Date Published: 2 March 2018
PDF: 9 pages
Proc. SPIE 10574, Medical Imaging 2018: Image Processing, 1057418 (2 March 2018); doi: 10.1117/12.2293920
Show Author Affiliations
Wei Shao, The Univ. of Iowa (United States)
Sarah E. Gerard, The Univ. of Iowa (United States)
Yue Pan, The Univ. of Iowa (United States)
Taylor J. Patton, Univ. of Wisconsin-Madison (United States)
Joseph M. Reinhardt, The Univ. of Iowa (United States)
Oguz C. Durumeric, The Univ. of Iowa (United States)
John E. Bayouth, Univ. of Wisconsin-Madison (United States)
Gary E. Christensen, The Univ. of Iowa (United States)

Published in SPIE Proceedings Vol. 10574:
Medical Imaging 2018: Image Processing
Elsa D. Angelini; Bennett A. Landman, Editor(s)

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