Segmentation of MS imaging experiments with Cardinal
Revised: September 12, 2024
Contents
1 Introduction
The goal of unsupervised analysis of mass spectrometry (MS) imaging experiments is to discover regions in the data with distinct chemical profiles, and to select the m/z values that uniquely distinguish these different regions from each other.
Algorithmically, this means clustering the data. In imaging experiments, the resulting cluster configurations are called spatial segmentations, and the clusters are called segments.
In this vignette, we present an example segmentation workflow using Cardinal.
We begin by loading the package:
library(Cardinal)2 Segmentation of a pig fetus wholy body cross section
This example uses the PIGII_206 dataset: a cross section of a pig fetus captured using a Thermo LTQ instrument using desorption electrospray ionization (DESI).
First, we load the dataset from the CardinalWorkflows package using exampleMSIData().
pig206 <- CardinalWorkflows::exampleMSIData("pig206")The dataset contains 4,959 spectra with 10,200 m/z values.
pig206## MSImagingExperiment with 10200 features and 4959 spectra
## spectraData(1): intensity
## featureData(1): mz
## pixelData(3): x, y, run
## coord(2): x = 10...120, y = 1...66
## runNames(1): PIGII_206
## mass range: 150.0833 to 1000.0000
## centroided: FALSE
In the optical image shown above, the brain (left), heart (center), and liver (large dark region) are clearly visible.
image(pig206, mz=885.5, tolerance=0.5, units="mz")
The dataset has been cropped to remove the background slide pixels, leaving only the tissue section itself for analysis.
2.1 Pre-processing
For statistical analysis, it is useful to reduce the dataset to include only the peaks.
We calculate the mean spectrum using summarizeFeatures().
pig206 <- summarizeFeatures(pig206, c(Mean="mean"))plot(pig206, "Mean", xlab="m/z", ylab="Intensity")
In order to make the mass spectra comparable between different pixels, it is necessary to normalize the data. We will use TIC normalization.
Let’s calculate the TIC to see how it currently varies across the dataset in the raw, unprocessed specra.
pig206 <- summarizePixels(pig206, c(TIC="sum"))image(pig206, "TIC")
To process the dataset, we will use peakProcess() to perform peak picking on a subset of the mass spectra, and then use these as a reference to summarize the peaks in every mass spectrum in the dataset.
We use sampleSize=0.1 to indicate we want to perform peak picking on 10% of spectra to create the reference peaks. SNR=3 indicates the signal-to-noise ratio threshold to peak detection. And tolerance=0.5 indicates the minimum distance between peaks. (Peaks closer together than this are merged.)
pig206_peaks <- pig206 |>
normalize(method="tic") |>
peakProcess(SNR=3, sampleSize=0.1,
tolerance=0.5, units="mz")
pig206_peaks## MSImagingExperiment with 687 features and 4959 spectra
## spectraData(1): intensity
## featureData(3): mz, count, freq
## pixelData(4): x, y, run, TIC
## coord(2): x = 10...120, y = 1...66
## runNames(1): PIGII_206
## metadata(1): processing_20241105111456
## mass range: 150.2917 to 999.8333
## centroided: TRUEThis produces a centroided dataset with 687 peaks.
2.2 Visualization
Before proceeding with the statistical analysis, we’ll first perform some and exploratory visual analysis of the dataset.
2.2.1 Ion images
Below, we plot several hand-selected peaks corresponding to major organs.
m/z 187 appears highly abundant in the heart.
image(pig206_peaks, mz=187.36)
m/z 840 appears highly abundant in the brain and spinal cord.
image(pig206_peaks, mz=840.43)
m/z 537 appears highly abundant in the liver.
image(pig206_peaks, mz=537.08)
Rather than manually going the full dataset and hand-selecting peaks, the goal of our statistical analysis will be to automatically select the peaks that distinguish such regions (e.g., the major organs).
2.2.2 Principal components analysis (PCA)
Principal component analysis (PCA) is a popular method for exploring a dataset. PCA is available in Cardinal through the PCA() method.
Below, we calculate the first 3 principal components.
pig206_pca <- PCA(pig206_peaks, ncomp=3)
pig206_pca## SpatialPCA on 687 variables and 4959 observations
## names(5): sdev, rotation, center, scale, x
## coord(2): x = 10...120, y = 1...66
## runNames(1): PIGII_206
## modelData(): Principal components (k=3)
##
## Standard deviations (1, .., k=3):
## PC1 PC2 PC3
## 56.48327 32.37418 21.94714
##
## Rotation (n x k) = (687 x 3):
## PC1 PC2 PC3
## [1,] 0.0065471300 0.0070376319 -0.0006104186
## [2,] 0.0500922072 -0.0080335867 -0.0202450539
## [3,] 0.0509196160 -0.0320650258 -0.0269319572
## [4,] 0.0198012214 -0.0135729648 -0.0088659582
## [5,] 0.0349473853 0.0050267457 0.0106713568
## [6,] 0.0636922031 0.0229462193 -0.0373597312
## ... ... ... ...Next, we overlay the first 3 principal components.
image(pig206_pca, smooth="adaptive", enhance="histogram")
We can plot the loadings for the principal components as well.
plot(pig206_pca, linewidth=2)
PCA can sometimes be useful for exploring a dataset. For example, here, we can see that PC3 appears to distinguish the liver, but also includes other structures. This makes it difficult to fully utilize PCA for analysis.
2.2.3 Non-negative matrix factorization (NMF)
Non-negative matrix factorization (NMF) is a popular alternative to PCA. It is similar to PCA, but produces non-negative loadings, which can make it easier to interpret and more suited to spectral data. NMF is available in Cardinal through the NMF() method.
Below, we calculate the first 3 NMF components.
pig206_nmf <- NMF(pig206_peaks, ncomp=3, niter=30)
pig206_nmf## SpatialNMF on 687 variables and 4959 observations
## names(4): activation, x, iter, transpose
## coord(2): x = 10...120, y = 1...66
## runNames(1): PIGII_206
## modelData(): Non-negative matrix factorization (k=3)
##
## Activation (n x k) = (687 x 3):
## C1 C2 C3
## [1,] 0.6071011 0.2020845 0.0000000
## [2,] 1.8608954 2.6511342 0.0000000
## [3,] 0.5065333 2.9905795 0.0000000
## [4,] 0.1363037 1.1769158 0.0000000
## [5,] 2.4890613 1.8862063 0.1213924
## [6,] 4.1351156 2.8922698 0.0000000
## ... ... ... ...Next, we overlay the first 3 NMF components.
image(pig206_nmf, smooth="adaptive", enhance="histogram")
We can plot the loadings for the NMF components as well.
plot(pig206_nmf, linewidth=2)
NMF seems to distinguish the morphology better than PCA in this case.
2.3 Segmentation with spatial shrunken centroids (SSC)
To segment the dataset and automatically select peaks that distinguish each region, we will use the spatialShrunkenCentroids() method provided by Cardinal.
Important parameters to this method include:
weightsThe type of spatial weights to use:“gaussian” weights use a simple Gaussian smoothing kernel
“adaptive” weights use an adaptive kernel that sometimes preserve edges better
rThe neighborhood smoothing radius; this should be selected based on the size and granularity of the spatial regions in your datasetkThe maximum number of segments to try; empty segments are dropped, so the resulting segmentation may use fewer than this number.sThe shrinkage or sparsity parameter; the higher this number, the fewer peaks will be used to determine the final segmentation.
It can be usefel to set k relatively high and let the algorithm drop empty segments. You typically want to try a wide range of sparsity with the s parameter.
set.seed(1)
pig206_ssc <- spatialShrunkenCentroids(pig206_peaks,
weights="adaptive", r=2, k=8, s=2^(1:6))
pig206_ssc## ResultsList of length 6
## names(6): r=2,k=8,s=2 r=2,k=8,s=4 r=2,k=8,s=8 r=2,k=8,s=16 r=2,k=8,s=32 r=2,k=8,s=64
## model: SpatialShrunkenCentroids
## r k s weights clusters sparsity AIC BIC
## r=2,k=8,s=2 2 8 2 adaptive 8 0.24 9829.304 41319.650
## r=2,k=8,s=4 2 8 4 adaptive 8 0.43 7767.168 32514.232
## r=2,k=8,s=8 2 8 8 adaptive 8 0.68 5119.647 20962.454
## r=2,k=8,s=16 2 8 16 adaptive 8 0.88 3212.689 11804.516
## r=2,k=8,s=32 2 8 32 adaptive 6 0.97 2371.056 7773.492
## r=2,k=8,s=64 2 8 64 adaptive 3 0.99 3586.159 8220.538This produces a ResultsList of the 6 fitted models.
As shown in the metadata columns, the number of resulting segments (clusters) is fewer for higher values of s. This is because fewer peaks are used to determine the segmentation.
Larger values of s will remove non-informative peaks, but very large values of s may remove meaningful peaks too. For very large values of s, morphological structures will begin to disappear from the segmentation. The most interesting and useful segmentations tend to be the ones with the highest value of s that still show meaningful morphology.
We can also look at the AIC and BIC values to help guide our choice of what segmentation to explore further. Smaller values are better, but small differences become less meaningful.
In this case, the last 2 models (s=32 and s=64) seem to be much better from the previous models. However, the model for s=32 supports 6 segments, while the model for s=64 only supports 3 segments.
2.3.1 Plotting the segmentation
Let’s plot the 4 most sparse segmentations.
image(pig206_ssc, i=3:6)
It is useful to see how the segmentation changes as fewer peaks are used and the number of segments decreases. Noisy, less-meaningful segments tend to be removed first, so we want to explore the segmentation with the highest value of s that still captures the morphology we would expect to see. At s=64, the heart segment is lost. We will choose the most sparse segmentation that still includes the heart.
pig206_ssc1 <- pig206_ssc[[5]]
image(pig206_ssc1)
Note that the translucent colors that don’t appear to belong to any segment indicate areas of low probability (i.e., high uncertainty in the segmentation).
We can plot the segment assignments instead of the probabilities to see the exact segmentation.
image(pig206_ssc1, type="class")
Here, we can see the liver, heart, and brain distinguished as segments 4, 5, and 6.
2.3.2 Plotting the (shrunken) mean spectra
Plotting the shrunken centroids is analogous to plotting the mean spectrum of each segment.
plot(pig206_ssc1, type="centers", linewidth=2)
Let’s break out the centroids for the liver, heart, and brain segments (4, 5, and 6).
plot(pig206_ssc1, type="centers", linewidth=2,
select=c(4,5,6), superpose=FALSE, layout=c(1,3))
Some differences are visible, but it can be difficult to tell exactly which peaks are changing between different segments based on the (shrunken) mean spectra alone.
2.3.3 Plotting and interpretting t-statistics of the m/z values
Plotting the t-statistics tells us exactly the relationship between each segment’s centroid and the global mean spectrum. The t-statistics are the difference between a segment’s centroid and the global mean, divided by a standard error.
Positive t-statistics indicate that peak is systematically higher intensity in that segment relative to the (global) mean spectrum.
Negative t-statistics indicate that peak is systematically lower intensity in that segment relative to the (global) mean spectrum.
Spatial shrunken centroids works by shrinking these t-statistics toward 0 by s, and using the new t-statistics to recompute the segment centroids. The effect is that peaks that are not very different between a specific segment and the global mean are effectively eliminated from the segmentation.
plot(pig206_ssc1, type="statistic", linewidth=2)
If we break out the t-statistics for the heart, liver, and brain segments we can learn something interesting.
plot(pig206_ssc1, type="statistic", linewidth=2,
select=c(4,5,6), superpose=FALSE, layout=c(1,3))
Very few peaks distinguish the heart (segment 5), while many more distinguish the liver and brain (segments 4 and 6).
2.3.4 Retrieving the top m/z values
Use the topFeatures() method to extract the m/z values of the peaks that most distinguish each segment, ranked by t-statistic.
pig206_ssc_top <- topFeatures(pig206_ssc1)Peaks associated with the liver:
subset(pig206_ssc_top, class==4 & statistic > 0)## DataFrame with 32 rows and 6 columns
## i mz class statistic centers sd
## <integer> <numeric> <character> <numeric> <numeric> <numeric>
## 1 289 537.106 4 118.1747 25.7564 2.96740
## 2 287 535.136 4 108.0515 18.2497 2.20841
## 3 306 563.077 4 107.4249 22.9829 3.00747
## 4 269 509.032 4 64.6042 11.2577 1.62113
## 5 83 253.573 4 44.8462 15.4211 2.81615
## ... ... ... ... ... ... ...
## 28 470 773.540 4 11.09341 2.89115 1.09850
## 29 579 889.566 4 8.08681 4.53182 1.75686
## 30 297 549.093 4 7.22217 3.92227 1.26671
## 31 270 510.239 4 5.56819 2.58318 1.13918
## 32 291 539.149 4 3.83563 4.79113 1.46118Peaks associated with the heart:
subset(pig206_ssc_top, class==5 & statistic > 0)## DataFrame with 2 rows and 6 columns
## i mz class statistic centers sd
## <integer> <numeric> <character> <numeric> <numeric> <numeric>
## 1 30 187.360 5 45.2865 48.04289 9.07711
## 2 29 186.358 5 22.0932 8.36483 2.39535Peaks associated with the brain:
subset(pig206_ssc_top, class==6 & statistic > 0)## DataFrame with 20 rows and 6 columns
## i mz class statistic centers sd
## <integer> <numeric> <character> <numeric> <numeric> <numeric>
## 1 533 840.431 6 36.8424 11.5145 3.07742
## 2 531 838.411 6 31.4069 7.7430 2.25276
## 3 575 885.568 6 31.3095 20.9094 6.25210
## 4 527 834.425 6 30.5606 10.0616 3.82043
## 5 128 305.472 6 30.1676 11.9883 3.24396
## ... ... ... ... ... ... ...
## 16 463 766.396 6 4.784931 6.33422 1.93903
## 17 150 333.582 6 4.548003 3.35320 1.92260
## 18 505 811.448 6 3.872509 4.05674 2.23656
## 19 529 836.311 6 1.302794 7.31574 2.51954
## 20 532 839.461 6 0.409365 3.02466 1.77519The top m/z values for each segment match up well with the hand-selected peaks.
3 Segmentation of a cardinal painting
It can be difficult to evaluate unsupervised methods (like segmentation) on data where we do not know the ground truth.
In this section, we use an MS image of a painting, where we know the ground truth.
cardinal <- CardinalWorkflows::exampleMSIData("cardinal")
In this experiment, DESI spectra were collected from an oil painting of a cardinal.
cardinal## MSImagingExperiment with 10800 features and 12600 spectra
## spectraData(1): intensity
## featureData(1): mz
## pixelData(3): x, y, run
## coord(2): x = 1...120, y = 1...105
## runNames(1): Bierbaum_demo_
## mass range: 100.0833 to 1000.0000
## centroided: FALSEThe dataset includes 12,600 spectra with 10,800 m/z values.
3.1 Pre-processing
We will begin by visualizing the mean spectrum as before.
cardinal <- summarizeFeatures(cardinal, c(Mean="mean"))plot(cardinal, "Mean", xlab="m/z", ylab="Intensity")
And the total ion current.
cardinal <- summarizePixels(cardinal, c(TIC="sum"))image(cardinal, "TIC")
We will pre-process the dataset as before, by applying peak picking to 10% of the spectra and then summarizing these peaks for every spectrum.
cardinal_peaks <- cardinal |>
normalize(method="tic") |>
peakProcess(SNR=3, sampleSize=0.1,
tolerance=0.5, units="mz")
cardinal_peaks## MSImagingExperiment with 929 features and 12600 spectra
## spectraData(1): intensity
## featureData(3): mz, count, freq
## pixelData(4): x, y, run, TIC
## coord(2): x = 1...120, y = 1...105
## runNames(1): Bierbaum_demo_
## metadata(1): processing_20241105111623
## mass range: 100.9923 to 999.5854
## centroided: TRUEThis results in a centroided dataset with 929 peaks.
3.2 Segmentation with SSC
Now we use spatial shrunken centroids to segment the dataset.
set.seed(1)
cardinal_ssc <- spatialShrunkenCentroids(cardinal_peaks,
weights="adaptive", r=2, k=8, s=2^(1:6))## Warning: Quick-TRANSfer stage steps exceeded maximum (= 630000)cardinal_ssc## ResultsList of length 6
## names(6): r=2,k=8,s=2 r=2,k=8,s=4 r=2,k=8,s=8 r=2,k=8,s=16 r=2,k=8,s=32 r=2,k=8,s=64
## model: SpatialShrunkenCentroids
## r k s weights clusters sparsity AIC BIC
## r=2,k=8,s=2 2 8 2 adaptive 8 0.59 9517.270 38881.24
## r=2,k=8,s=4 2 8 4 adaptive 8 0.81 6498.761 23695.96
## r=2,k=8,s=8 2 8 8 adaptive 8 0.92 5621.878 16687.32
## r=2,k=8,s=16 2 8 16 adaptive 8 0.97 6448.393 15162.33
## r=2,k=8,s=32 2 8 32 adaptive 7 0.98 7817.986 15482.68
## r=2,k=8,s=64 2 8 64 adaptive 5 0.99 6952.329 14133.33image(cardinal_ssc, i=3:6)
We can see increasing higher sparsities result in lose the “wing” segment, so we will choose the most sparse segmentation that retains the cardinal’s wings.
Now we can use the segmentation to re-construct the original painting.
cardinal_ssc1 <- cardinal_ssc[[3]]
pal <- c("1"=NA, "2"="firebrick", "3"=NA, "4"="black",
"5"="red", "6"="gray", "7"=NA, "8"="darkred")
image(cardinal_ssc1, col=pal)
Let’s find the m/z values associated with the cardinal’s body.
cardinal_ssc_top <- topFeatures(cardinal_ssc1)
subset(cardinal_ssc_top, class==5)## DataFrame with 929 rows and 6 columns
## i mz class statistic centers sd
## <integer> <numeric> <character> <numeric> <numeric> <numeric>
## 1 100 207.051 5 254.262 233.1202 22.4128
## 2 169 277.033 5 211.766 139.1255 15.0486
## 3 182 290.988 5 175.537 105.2283 12.7141
## 4 297 418.874 5 154.018 98.9911 14.8391
## 5 216 327.133 5 117.054 66.5980 10.4429
## ... ... ... ... ... ... ...
## 925 50 157.098 5 -80.4969 31.1409 19.2454
## 926 175 283.239 5 -81.6780 18.3817 18.5401
## 927 134 241.153 5 -84.1666 15.4854 15.6296
## 928 120 227.182 5 -97.8311 18.7459 18.5312
## 929 148 255.229 5 -124.9192 34.8702 31.3986image(cardinal_peaks, mz=207.05, smooth="guided", enhance="histogram")
And let’s find the m/z values associated with the “DESI-MS” text.
subset(cardinal_ssc_top, class==2)## DataFrame with 929 rows and 6 columns
## i mz class statistic centers sd
## <integer> <numeric> <character> <numeric> <numeric> <numeric>
## 1 487 648.999 2 161.4926 269.9236 36.57814
## 2 488 650.155 2 124.4383 101.7906 14.95678
## 3 489 651.132 2 40.3626 20.6268 6.10854
## 4 336 473.026 2 29.2708 19.5684 8.13424
## 5 503 664.751 2 26.4676 13.8407 5.81793
## ... ... ... ... ... ... ...
## 925 175 283.239 2 -26.1172 50.5043 18.5401
## 926 162 269.155 2 -26.9751 23.5159 12.3435
## 927 134 241.153 2 -40.2095 34.7970 15.6296
## 928 120 227.182 2 -46.9775 44.0954 18.5312
## 929 148 255.229 2 -51.1971 95.9676 31.3986image(cardinal_peaks, mz=648.99, smooth="guided", enhance="histogram")
4 Session information
sessionInfo()## R Under development (unstable) (2024-10-21 r87258)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.1 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.21-bioc/R/lib/libRblas.so
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0
##
## Random number generation:
## RNG: L'Ecuyer-CMRG
## Normal: Inversion
## Sample: Rejection
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_GB LC_COLLATE=C
## [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## time zone: America/New_York
## tzcode source: system (glibc)
##
## attached base packages:
## [1] stats4 stats graphics grDevices utils datasets methods
## [8] base
##
## other attached packages:
## [1] Cardinal_3.9.0 S4Vectors_0.45.0 ProtGenerics_1.39.0
## [4] BiocGenerics_0.53.1 generics_0.1.3 BiocParallel_1.41.0
## [7] BiocStyle_2.35.0
##
## loaded via a namespace (and not attached):
## [1] sass_0.4.9 tiff_0.1-12 bitops_1.0-9
## [4] jpeg_0.1-10 lattice_0.22-6 digest_0.6.37
## [7] magrittr_2.0.3 evaluate_1.0.1 grid_4.5.0
## [10] bookdown_0.41 fftwtools_0.9-11 fastmap_1.2.0
## [13] jsonlite_1.8.9 Matrix_1.7-1 ontologyIndex_2.12
## [16] CardinalWorkflows_1.39.0 matter_2.9.0 tinytex_0.54
## [19] BiocManager_1.30.25 codetools_0.2-20 jquerylib_0.1.4
## [22] abind_1.4-8 cli_3.6.3 rlang_1.1.4
## [25] CardinalIO_1.5.0 Biobase_2.67.0 EBImage_4.49.0
## [28] cachem_1.1.0 yaml_2.3.10 tools_4.5.0
## [31] parallel_4.5.0 locfit_1.5-9.10 R6_2.5.1
## [34] png_0.1-8 lifecycle_1.0.4 magick_2.8.5
## [37] htmlwidgets_1.6.4 irlba_2.3.5.1 bslib_0.8.0
## [40] Rcpp_1.0.13-1 xfun_0.49 highr_0.11
## [43] knitr_1.48 htmltools_0.5.8.1 nlme_3.1-166
## [46] rmarkdown_2.29 compiler_4.5.0 RCurl_1.98-1.16