Detecting cells using non-negative matrix factorization on calcium imaging data
Introduction
Ca2+ imaging techniques enable us to measure the temporal variation in the intracellular Ca2+ concentration (Grynkiewicz, Poenie, & Tsien, 1985). In the case of nerve cells, the intracellular Ca2+ concentration is closely related to the membrane potential of cells because Ca2+ is recruited inside through voltage-dependent Ca2+ channels whose conductivities depend on the membrane potential. Therefore, the instantaneous elevation of the intracellular Ca2+ concentration gives us important information on the time of action potential generation. Many research groups have developed multi-cellular Ca2+ imaging systems to record individual cellular activities of a cell assembly in vitro and in vivo. For example, Ikegaya et al. (2004), Ikegaya, Le Bon-Jego, and Yuste (2005) recorded the spike times of hundreds of cortical neurons in in vitro Ca2+ imaging and discovered a repeated firing sequence from particular groups of neurons. Dombeck, Harvey, Tian, Looger, and Tank (2010) recorded in vivo hippocampal CA1 neurons of a moving rat and showed the spatial distribution of place cells. Furthermore, our group has developed a multi-cellular Ca2+ recording system able to record from dendritic tufts as well as somas (Maeda et al., submitted for publication, Maeda et al., 2012). Thus, Ca2+ imaging can also be used to record the activities of subcellular structures of multiple cells in a wide area.
The first step of a typical analysis of multi-cellular Ca2+ imaging data is the identification of the positions of individual cells as regions of interest (ROIs) within the image; this step is called ‘cell detection’ (Lutcke & Helmchen, 2011). In almost all of the related studies, experimenters searched for cells by inspecting the movie data with the naked eye, and they manually identified ROIs in the movie frames. This manual method is very effective but it needs of a lot of time and effort. The rapid progress of imaging systems has made it possible for us to record high spatial and temporal resolution imaging data for a long time (Ziv et al., 2013). However, the rapid increase in the data volume makes it very difficult for us to analyze the imaging data manually. This has meant that automatic or semi-automatic methods of cell detection have become increasingly necessary.
To overcome this issue, many research groups have devised sophisticated statistical algorithms (Junek et al., 2009, Miri et al., 2011, Miri et al., 2011, Mukamel et al., 2009, Ozden et al., 2008, Reidl et al., 2007, Valmianski et al., 2010, Vogelstein et al., 2010). Some research groups have demonstrated the effectiveness of independent component analysis (ICA) on high spatial and temporal resolution imaging data (Mukamel et al., 2009, Reidl et al., 2007). In particular, Mukamel et al. (2009) proposed an automated image segmentation method based on ICA that provides a fast and efficient strategy for analyzing large-scale calcium imaging data sets (Lutcke & Helmchen, 2011). ICA was first used to detect cells in low-resolution imaging data about a decade ago (Brown, Yamada, & Sejnowski, 2001). A revival in interest in ICA began with Mukamel’s work (Dombeck et al., 2010, Ziv et al., 2013). This algorithm initially performs the principal component analysis (PCA) to reduce the dimensions of the data, and after that it executes a joint maximization of two objective functions, spatial skewness and temporal skewness. The performance of this algorithm depends on the number of principal components and the parameter for tuning the priorities between the two objective functions, and users need to fine-tune them.
The aim of this study is to establish a reliable method that detects the position of cells automatically from such a high-resolution multi-cellular Ca2+ imaging data. Our cell detection algorithm based on non-negative matrix factorization (NMF), which is a low rank matrix decomposition method that restricts the component matrices to have non-negative values (Lee & Seung, 1999). NMF is a well-known algorithm that is useful for separating image data into constitutive parts (Hoyer, 2004). To apply it to calcium imaging movie data, we introduced a background constraint: the bleaching line of the background fluorescence intensity, which can be estimated directly from the imaging data, is given as an a priori background constraint to uniquely dissociate the background component from the image data. This constraint helps to reduce the non-uniqueness of the solution, which is known to be a big problem of factorization (Benzi, 2002). The advantages of this method are that (1) it involves no parameter that needs tuning, except for the number of cells, (2) model order selection can (in principle) be used to determine the number of cells, and (3) it can incorporate the effect of dye-bleaching as a result of being given the bleaching line of the background as a constraint.
In this paper, we compare the performances of the NMF algorithm and the state-of-art ICA algorithm on simulated movie data. We demonstrate that in the case of noisy data, the NMF algorithm can detect cells more accurately than the optimally tuned ICA algorithm, and in the low-noise case, the NMF algorithm almost as well as the ICA algorithm. After that, we apply the NMF algorithm to high-resolution Ca2+ imaging data recording the local activities of subcellular structures of multiple cells in a wide area. We demonstrate that our method can decompose rapid transient components corresponding to somas and dendrites of different active neurons, and furthermore, it can decompose slow transient components probably corresponding to glial cells.
Section snippets
Cell detection by non-negative matrix factorization
Here, we modify the NMF algorithm so that it can be applied to Ca2+ imaging data. Let us consider a case in which a two-dimensional calcium imaging movie consists of frames in total and each frame consists of pixels. The two-dimensional array of pixels in each frame is rearranged to form a one-dimensional column vector, and a data matrix ( by ) is obtained. For the sake of simplicity, we assume that is the sum of fluorescence signals from cells labeled 1–, background fluorescence,
Comparison of NMF and ICA algorithms using artificial imaging data
We applied the NMF algorithm and the Mukamel’s ICA algorithm to the simulated image data and compared their performances. The number of cells was set to be eight when the artificial image data was generated. We used the following parameter settings. For the NMF algorithm, the number of components was set to , and the time course of static background fluorescence intensity was given a priori as the background constraint. For comparison, we tried to test the NMF with one excess ordinary
Summary of the results and conclusion
We developed an algorithm for detecting cells in calcium imaging data. The algorithm is based on NMF, which is a low rank matrix decomposition that restricts the component matrices to have non-negative values. To apply NMF to Ca2+ imaging data, we introduced a background constraint: the bleaching line of the background fluorescence intensity is given a priori as a constraint to uniquely dissociate the background component from the image data. This constraint helps us to incorporate the effect
Acknowledgment
This work was supported by JSPS KAKENHI Grant Number 23500375.
References (29)
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
(2002)- et al.
Algorithms and applications for approximate nonnegative matrix factorization
Computational Statistics & Data Analysis
(2007) - et al.
Independent component analysis at the neural cocktail party
Trends in Neurosciences
(2001) - et al.
A new generation of indicators with greatly improved fluorescence properties
Journal of Biological Chemistry
(1985) - et al.
Large-scale imaging of cortical network activity with calcium indicatorslarge-scale imaging of cortical network activity with calcium indicators
Neuroscience Research
(2005) - et al.
Activity correlation imaging: visualizing function and structure of neuronal populations
Biophysical Journal
(2009) - et al.
Automated analysis of cellular signals from large-scale calcium imaging data
Neuron
(2009) - et al.
Selective fura-2 loading of presynaptic terminals and nerve cell processes by local perfusion in mammalian brain slice
Journal of Neuroscience Methods
(1991) - et al.
Independent component analysis of high-resolution imaging data identifies distinct functional domains
Neuroimage
(2007) - Canny, J.F. (2004). Gap: a factormodel for discrete data. In 27th ACM Int. Conf. Res. Develop. Inform. Retrieval...
Bayesian inference for nonnegative matrix factorisation models
Computational Intelligence and Neuroscience
Functional imaging of hippocampal place cells at cellular resolution during virtual navigation
Nature Neuroscience
Non-negative matrix factorization with sparseness constraints
Journal of Machine Learning Research
Independent component analysis
Cited by (100)
Extraction of bouton-like structures from neuropil calcium imaging data
2022, Neural NetworksCitation Excerpt :In addition, various imaging data decomposition algorithms are based on the assumption that there is a background space between cell bodies. For example, an NMF-based algorithm by Maruyama et al. (2014) includes background components, and the activity-based level set segmentation (ABLE) (Reynolds et al., 2017) detects regions on the premise that the target regions are surrounded by background regions. In contrast, boutons were densely packed in the neuropil images, and there was no space between boutons, which would make CNMF and other decomposition algorithms hard to segregate individual boutons.
Low computational-cost cell detection method for calcium imaging data
2022, Neuroscience ResearchFast z-focus controlling and multiplexing strategies for multiplane two-photon imaging of neural dynamics
2022, Neuroscience ResearchImaging data analysis using non-negative matrix factorization
2022, Neuroscience ResearchCitation Excerpt :These results have had a large impact on the field of neuroscience and triggered the following research. Maruyama et al. (2014) developed non-negative matrix factorization (NMF) with a background constraint (called background constrained NMF (BCNMF)) that could detect weak cell signals compared with a background signal (Maeda et al., 2015). Pnevmatikakis et al. (2016) proposed constrained NMF (CNMF) in which calcium transient dynamics are incorporated as an autoregressive model.
Machine learning data processing as a bridge between microscopy and the brain
2022, Intelligent Nanotechnology: Merging Nanoscience and Artificial Intelligence