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December 2009 Use of multiple singular value decompositions to analyze complex intracellular calcium ion signals
Josue G. Martinez, Jianhua Z. Huang, Robert C. Burghardt, Rola Barhoumi, Raymond J. Carroll
Ann. Appl. Stat. 3(4): 1467-1492 (December 2009). DOI: 10.1214/09-AOAS253


We compare calcium ion signaling (Ca2+) between two exposures; the data are present as movies, or, more prosaically, time series of images. This paper describes novel uses of singular value decompositions (SVD) and weighted versions of them (WSVD) to extract the signals from such movies, in a way that is semi-automatic and tuned closely to the actual data and their many complexities. These complexities include the following. First, the images themselves are of no interest: all interest focuses on the behavior of individual cells across time, and thus, the cells need to be segmented in an automated manner. Second, the cells themselves have 100+ pixels, so that they form 100+ curves measured over time, so that data compression is required to extract the features of these curves. Third, some of the pixels in some of the cells are subject to image saturation due to bit depth limits, and this saturation needs to be accounted for if one is to normalize the images in a reasonably unbiased manner. Finally, the Ca2+ signals have oscillations or waves that vary with time and these signals need to be extracted. Thus, our aim is to show how to use multiple weighted and standard singular value decompositions to detect, extract and clarify the Ca2+ signals. Our signal extraction methods then lead to simple although finely focused statistical methods to compare Ca2+ signals across experimental conditions.


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Josue G. Martinez. Jianhua Z. Huang. Robert C. Burghardt. Rola Barhoumi. Raymond J. Carroll. "Use of multiple singular value decompositions to analyze complex intracellular calcium ion signals." Ann. Appl. Stat. 3 (4) 1467 - 1492, December 2009.


Published: December 2009
First available in Project Euclid: 1 March 2010

zbMATH: 1185.92074
MathSciNet: MR2752142
Digital Object Identifier: 10.1214/09-AOAS253

Keywords: Calcium ion signaling , myometrial cells , semi-automatic segmentation , Singular value decomposition , weighted SVD

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.3 • No. 4 • December 2009
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