Testing for Multivariate Normality in Mass Spectrometry Imaging Data: A Robust Statistical Approach for Clustering Evaluation and the Generation of Synthetic Mass Spectrometry Imaging Data Sets

Spatial clustering is a powerful tool in mass spectrometry imaging (MSI) and has been demonstrated to be capable of differentiating tumor types, visualizing intratumor heterogeneity, and segmenting anatomical structures. Several clustering methods have been applied to mass spectrometry imaging data, but a principled comparison and evaluation of different clustering techniques presents a significant challenge. We propose that testing whether the data has a multivariate normal distribution within clusters can be used to evaluate the performance when using algorithms that assume normality in the data, such as <i>k</i>-means clustering. In cases where clustering has been performed using the cosine distance, conversion of the data to polar coordinates prior to normality testing should be performed to ensure normality is tested in the correct coordinate system. In addition to these evaluations of internal consistency, we demonstrate that the multivariate normal distribution can then be used as a basis for statistical modeling of MSI data. This allows the generation of synthetic MSI data sets with known ground truth, providing a means of external clustering evaluation. To demonstrate this, reference data from seven anatomical regions of an MSI image of a coronal section of mouse brain were modeled. From this, a set of synthetic data based on this model was generated. Results of <i>r</i>² fitting of the chi-squared quantile–quantile plots on the seven anatomical regions confirmed that the data acquired from each spatial region was found to be closer to normally distributed in polar space than in Euclidean. Finally, principal component analysis was applied to a single data set that included synthetic and real data. No significant differences were found between the two data types, indicating the suitability of these methods for generating realistic synthetic data

MALDI Imaging of Liquid Extraction Surface Analysis Sampled Tissue

Combined mass spectrometry imaging methods in which two different techniques are executed on the same sample have recently been reported for a number of sample types. Such an approach can be used to examine the sampling effects of the first technique with a second, higher resolution method and also combines the advantages of each technique for a more complete analysis. In this work matrix-assisted laser desorption ionization mass spectrometry imaging (MALDI MSI) was used to study the effects of liquid extraction surface analysis (LESA) sampling on mouse brain tissue. Complementary multivariate analysis techniques including principal component analysis, non-negative matrix factorization, and <i>t</i>-distributed stochastic neighbor embedding were applied to MALDI MS images acquired from tissue which had been sampled by LESA to gain a better understanding of localized tissue washing in LESA sampling. It was found that MALDI MS images could be used to visualize regions sampled by LESA. The variability in sampling area, spatial precision, and delocalization of analytes in tissue induced by LESA were assessed using both single-ion images and images provided by multivariate analysis

LESA FAIMS Mass Spectrometry for the Spatial Profiling of Proteins from Tissue

We have shown previously that coupling of high field asymmetric waveform ion mobility spectrometry (FAIMS), also known as differential ion mobility, with liquid extraction surface analysis (LESA) mass spectrometry of tissue results in significant improvements in the resulting protein mass spectra. Here, we demonstrate LESA FAIMS mass spectrometry imaging of proteins in sections of mouse brain and liver tissue. The results are compared with LESA mass spectrometry images obtained in the absence of FAIMS. The results show that the number of different protein species detected can be significantly increased by incorporating FAIMS into the workflow. A total of 34 proteins were detected by LESA FAIMS mass spectrometry imaging of mouse brain, of which 26 were unique to FAIMS, compared with 15 proteins (7 unique) detected by LESA mass spectrometry imaging. A number of proteins were identified including α-globin, 6.8 kDa mitochondrial proteolipid, macrophage migration inhibitory factor, ubiquitin, β-thymosin 4, and calmodulin. A total of 40 species were detected by LESA FAIMS mass spectrometry imaging of mouse liver, of which 29 were unique to FAIMS, compared with 24 proteins (13 unique) detected by LESA mass spectrometry imaging. The spatial distributions of proteins identified in both LESA mass spectrometry imaging and LESA FAIMS mass spectrometry imaging were in good agreement indicating that FAIMS is a suitable tool for inclusion in mass spectrometry imaging workflows

Raster-Mode Continuous-Flow Liquid Microjunction Mass Spectrometry Imaging of Proteins in Thin Tissue Sections

Mass spectrometry imaging by use of continuous-flow liquid microjunction sampling at discrete locations (array mode) has previously been demonstrated. In this Letter, we demonstrate continuous-flow liquid microjunction mass spectrometry imaging of proteins from thin tissue sections in raster mode and discuss advantages (a 10-fold reduction in analysis time) and challenges (suitable solvent systems, data interpretation) of the approach. Visualization of data is nontrivial, requiring correlation of solvent-flow, mass spectral data acquisition rate, data quality, and liquid microjunction sampling area. The latter is particularly important for determining optimum pixel size. The minimum achievable pixel size is related to the scan time of the instrument used. Here we show a minimum achievable pixel size of 50 μm (<i>x</i>-dimension) when using an Orbitrap Elite; however a pixel size of 600 μm is recommended in order to minimize the effects of oversampling on image accuracy

Memory Efficient Principal Component Analysis for the Dimensionality Reduction of Large Mass Spectrometry Imaging Data Sets

A memory efficient algorithm for the computation of principal component analysis (PCA) of large mass spectrometry imaging data sets is presented. Mass spectrometry imaging (MSI) enables two- and three-dimensional overviews of hundreds of unlabeled molecular species in complex samples such as intact tissue. PCA, in combination with data binning or other reduction algorithms, has been widely used in the unsupervised processing of MSI data and as a dimentionality reduction method prior to clustering and spatial segmentation. Standard implementations of PCA require the data to be stored in random access memory. This imposes an upper limit on the amount of data that can be processed, necessitating a compromise between the number of pixels and the number of peaks to include. With increasing interest in multivariate analysis of large 3D multislice data sets and ongoing improvements in instrumentation, the ability to retain all pixels and many more peaks is increasingly important. We present a new method which has no limitation on the number of pixels and allows an increased number of peaks to be retained. The new technique was validated against the MATLAB (The MathWorks Inc., Natick, Massachusetts) implementation of PCA (<i>princomp</i>) and then used to reduce, without discarding peaks or pixels, multiple serial sections acquired from a single mouse brain which was too large to be analyzed with <i>princomp</i>. Then, <i>k</i>-means clustering was performed on the reduced data set. We further demonstrate with simulated data of 83 slices, comprising 20 535 pixels per slice and equaling 44 GB of data, that the new method can be used in combination with existing tools to process an entire organ. MATLAB code implementing the memory efficient PCA algorithm is provided

Two-Phase and Graph-Based Clustering Methods for Accurate and Efficient Segmentation of Large Mass Spectrometry Images

Clustering is widely used in MSI to segment anatomical features and differentiate tissue types, but existing approaches are both CPU and memory-intensive, limiting their application to small, single data sets. We propose a new approach that uses a graph-based algorithm with a two-phase sampling method that overcomes this limitation. We demonstrate the algorithm on a range of sample types and show that it can segment anatomical features that are not identified using commonly employed algorithms in MSI, and we validate our results on synthetic MSI data. We show that the algorithm is robust to fluctuations in data quality by successfully clustering data with a designed-in variance using data acquired with varying laser fluence. Finally, we show that this method is capable of generating accurate segmentations of large MSI data sets acquired on the newest generation of MSI instruments and evaluate these results by comparison with histopathology