Cardinal is an R package for statistical analysis of mass spectrometry-based imaging (MSI) experiments of biological samples such as tissues. Cardinal supports both Matrix-Assisted Laser Desorption/Ionization (MALDI) and Desorption Electrospray Ionization-based MSI workflows, and experiments with multiple tissues and complex designs. The main analytical functionalities include (1) image segmentation, which partitions a tissue into regions of homogeneous chemical composition, selects the number of segments and the subset of informative ions, and characterizes the associated uncertainty and (2) image classification, which assigns locations on the tissue to pre-defined classes, selects the subset of informative ions, and estimates the resulting classification error by (cross-) validation. The statistical methods are based on mixture modeling and regularization.Contact: o.vitek@neu.eduAvailability and implementation: The code, the documentation, and examples are available open-source at www.cardinalmsi.org under the Artistic-2.0 license. The package is available at www.bioconductor.org.

Mass spectrometry imaging is a powerful tool for investigating the spatial distribution of chemical compounds in a biological sample such as tissue. Two common goals of these experiments are unsupervised segmentation of images into newly discovered homogeneous segments and supervised classification of images into predefined classes. In both cases, the important secondary goals are to characterize the uncertainty associated with the segmentation and with the classification and to characterize the spectral features that define each segment or class. Recent analysis methods have focused on the spatial structure of the data to improve results. However, they either do not address these secondary goals or do this with separate post hoc procedures.We introduce spatial shrunken centroids, a statistical model-based framework for both supervised classification and unsupervised segmentation. It takes as input sets of previously detected, aligned, quantified, and normalized spectral features and expresses both spatial and multivariate nature of the data using probabilistic modeling. It selects informative subsets of spectral features that define each unsupervised segment or supervised class and quantifies and visualizes the uncertainty in spatial segmentations and in tissue classification. In the unsupervised setting, it also guides the choice of an appropriate number of segments. We demonstrate the usefulness of this framework in a supervised human renal cell carcinoma experimental dataset and several unsupervised experimental datasets, including a pig fetus cross-section, three rodent brains, and a controlled image with known ground truth. This framework is available for use within the open-source R package Cardinal as part of a full pipeline for the processing, visualization, and statistical analysis of mass spectrometry imaging experiments.

Foodborne disease outbreaks of recent years demonstrate that due to increasingly interconnected supply chains these type of crisis situations have the potential to affect thousands of people, leading to significant healthcare costs, loss of revenue for food companies, and—in the worst cases—death. When a disease outbreak is detected, identifying the contaminated food quickly is vital to minimize suffering and limit economic losses. Here we present a likelihood-based approach that has the potential to accelerate the time needed to identify possibly contaminated food products, which is based on exploitation of food products sales data and the distribution of foodborne illness case reports. Using a real world food sales data set and artificially generated outbreak scenarios, we show that this method performs very well for contamination scenarios originating from a single “guilty” food product. As it is neither always possible nor necessary to identify the single offending product, the method has been extended such that it can be used as a binary classifier. With this extension it is possible to generate a set of potentially “guilty” products that contains the real outbreak source with very high accuracy. Furthermore we explore the patterns of food distributions that lead to “hard-to-identify” foods, the possibility of identifying these food groups a priori, and the extent to which the likelihood-based method can be used to quantify uncertainty. We find that high spatial correlation of sales data between products may be a useful indicator for “hard-to-identify” products.

Our aim in this paper is to investigate the boundedness, the extreme stability, and the periodicity of positive solutions of the periodically forced Sigmoid Beverton-Holt model:where {a n } is a positive periodic sequence with period p and δ > 0. In the special case when δ = 1, the above equation reduces to the well-known periodic Pielou logistic equation which is known to be equivalent to the periodically forced Beverton-Holt model.

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