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Computational and Mathematical Methods in Medicine
Volume 2013, Article ID 482941, 9 pages
Research Article

GND-PCA-Based Statistical Modeling of Diaphragm Motion Extracted from 4D MRI

1Graduate School of Engineering, Chiba University, Chiba 263-8522, Japan
2Chiba University Hospital, Chiba 260-8677, Japan
3Graduate School of Medicine, Yamaguchi University, Yamaguchi 755-8505, Japan
4Graduate School of Science and Engineering, Ritsumeikan University, Shiga 525-8577, Japan
5Research Center for Frontier Medical Engineering Chiba University, Chiba 263-8522, Japan

Received 18 January 2013; Revised 16 April 2013; Accepted 17 April 2013

Academic Editor: Chung-Ming Chen

Copyright © 2013 Windra Swastika et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We analyzed a statistical model of diaphragm motion using regular principal component analysis (PCA) and generalized N-dimensional PCA (GND-PCA). First, we generate 4D MRI of respiratory motion from 2D MRI using an intersection profile method. We then extract semiautomatically the diaphragm boundary from the 4D-MRI to get subject-specific diaphragm motion. In order to build a general statistical model of diaphragm motion, we normalize the diaphragm motion in time and spatial domains and evaluate the diaphragm motion model of 10 healthy subjects by applying regular PCA and GND-PCA. We also validate the results using the leave-one-out method. The results show that the first three principal components of regular PCA contain more than 98% of the total variation of diaphragm motion. However, validation using leave-one-out method gives up to 5.0 mm mean of error for right diaphragm motion and 3.8 mm mean of error for left diaphragm motion. Model analysis using GND-PCA provides about 1 mm margin of error and is able to reconstruct the diaphragm model by fewer samples.