Correlation analyses of MSI data

Modified correlation coefficient for higher contrast in pixels similarity

To demonstrate similarity in spectral profile of a pixel with the remainder of the sample, correlations (r) are calculated between the pixel of interest and all other pixels. The result of this pixel correlation is shown in the top of figure 5.10 for a pixel in the hippocampus: grey and white matter areas show up as highly correlated and anti-correlated, respectively. Here, it is proposed to employ enhanced correlations to get a clearer contrast of the different levels of correlation between pixels, an approach previously used in the evaluation of pharmaceutical tablets.238 _{This is done by} scaling the correlations between 0 to 1, representing the lowest and highest correlation, respectively, according to equation 5.2.

rscaled =_{max(r) − min(r)}r −min(r) (5.2)

Subsequently, an ‘enhanced correlation’ r_enh is obtained via equation 5.3, where α is a parameter governing the discrimination power: a value close to 0 implies high discrimination power, a value of α close to 1 will give a correlation profile similar to the original correlation coefficients.238

renh =_{max(rscaled) + α − rscaled}rscaled − min(rscaled) (5.3) This approach can be viewed as a non-linear transformation of the colour scale of the images, and will therefore not uncover new information, but enhance the contrast in the correlation figures.

The correlation enhancement was implemented for both Pearson and Spearman correlations, and the result is visible in figure 5.10. The top row shows the Pearson (left) and Spearman (right) correlations with the selected pixel, and a large number of correlated pixels are observed. The smaller plots indicate the evolution of the observed correlation profiles with increasing levels of α, where α = 1 is almost equivalent to the normal correlation profiles, highlighting all grey matter, and lower levels of α accentuate the hippocampus. This is exactly the use of correlation enhancement: small differences in correlation patterns are emphasised, to allow more differentiation between otherwise highly correlated regions. Notably, the Pearson and Spearman correlation patterns are

Figure 5.10: The Pearson (left) and Spearman (right) correlations of image pixels with a selected pixel (centre of white circle in the hippocampus). The smaller maps show images of the enhanced correlations for different levels ofα, see equations 5.2 and 5.3, for both the Pearson and Spearman correlation data.

very similar, but Spearman correlations need a higher α value to achieve the same pattern, e.g. compare α = 0.2 for Pearson with α = 0.5 for the Spearman correlation.

Figure 5.11 A shows the frequency histogram of the Pearson correlations from the pixel selected in figure 5.10 before correlation enhancement. The correlation was enhanced with α = 0.01 to create the histogram shown in figure 5.11 B, and an expansion is shown in figure 5.11 C. It is clear that the number of highly positively correlated peaks is greatly reduced after correlation enhancement, in correspondence with the analogous image for α = 0.01 in figure 5.10.

−10 −0.5 0 0.5 1 500 1000 correlation 0 0.5 1 0 2000 4000 6000 enhanced correlation 0 0.5 1 0 10 20 30 enhanced correlation

A

B

C

Figure 5.11: (A) Frequency histogram showing the distribution of Pearson correlation values before correlation enhancement (for the pixel selected in figure 5.10). (B) The frequency histogram after correlation enhancement withα =0.01. (C) An expansion of the histogram in B shows that the number of highly correlated peaks is greatly reduced compared to A.

STOCSYand the quality of MSI data

Correlation analysis of msi data has previously shown the ability to relate different m/z values based on co-localisation, and it was found that results of correlation analysis are greatly dependent on data processing steps, such as smoothing, baseline subtraction and normalisation.239 _The use of statistical total correlation spectroscopy (stocsy, see §2.3.7) to relate different molecular compounds was briefly evaluated for this msi data set, as similar spatial distributions of isotopes and fragments could help identification of unknowns. However, there are a number of effects that hinder the successful application of stocsy. Firstly, maldi is a soft ionisation approach and therefore there will not be many fragments, whereas e.g. in gc-ms there will be many fragments and in nmr there are often a number of resonances from one molecule. Additionally, adducts are formed in the ionisation step, for example the cationisation of the analyte with alkali metal ions such as potassium and sodium, dimerisation and other interactions with the maldi matrix solution. The formation of adducts is known to vary in different parts of the tissue, and this will negatively affect correlation approaches: if more sodium than potassium adduct is formed in one part of the tissue, and more potassium than sodium adduct in a second part, these peaks will show a low or even negative correlation. Studies have found that the distributions of metal adduct forms are different: the hippocampus had nearly twice as much potassium adduct of m/z = 734 as the protonated form, while the corpus callosum had nearly equal amounts.240 _{It could be an option to}

identify molecules by performing stocsy only on the pixels of a selected anatomical region (with comparable adduct formation), rather than on the complete image.

Matrix choice and application method are crucial determinants of the information obtained from the sample, in terms of measured (desorbed) metabolites as well as in terms of quantitation and reproducibility.206, 213 _{Spectral quality is additionally influenced by suppression effects, which} is that certain desorbed species can preferentially become ionised, and therefore appear to be at higher abundance in the spectrum; this process is at the cost of species that have lower ionisation efficiency and therefore appear to have lower relative abundances than the true sample composition. Suppression effects can differ between tissue types and analyte classes,226_{which can cause serious} artefacts when comparing regions and tissues in a quantitative manner. Thus, maldi imaging data should be treated as semi-quantitative, or qualitative, especially because the variable pixel quality can skew the distributions of peak intensity.