Fig 1.
CytoSpatio process for learning spatial relationships between different cell types.
(A) A region from a larger lymph node image is shown, with cell types shown in different colors and cell boundaries shown in white. The blue concentric circles denote five distance ranges of 100-500 pixels at 100-pixel intervals. (B) The training process involves counting the number of other cells of each type within varying distance ranges for each cell, as illustrated for the cell at the (small blue diamond) in panel A, a B cell. (C) A simplified version of the equation used for the fitting process in a point process model to learn the spatial relationships among cell types is shown. The probability of a particular cell type c at a given location, x, is given by a (global) base intensity
adjusted for the influence of (multiplied by) the local frequencies of all cell types. This adjustment is given by the dot product of a vector of interaction coefficients
for this cell type with all cell types (including its own) and a vector (Counts(x)) reflecting the counts of each cell type. The interaction coefficient and counts can be for a single range (i.e., one of the columns in panel B) or can be concatenated across multiple ranges (i.e., linearizing the counts in panel B). (D) Predicted intensities (proportional to the probabilities of occurrence) are shown for three cell types for each cell in this region (derived from a model trained with the entire image). Brighter colors indicate a higher predicted intensity, with each color corresponding to a distinct cell type. (E) A synthetic image depicting predicted cell types generated for this region from the model is shown. The image was generated from the model using the positions of each cell in panel A but assigning each cell’s type based on the predicted probabilities across the cell types for that location (cell type colors are the same as in panel (A)).
Table 1.
Comparison of average deviance per cell between shuffled point pattern sets and original point pattern sets. Lower average deviance per cell indicates a higher likelihood that a particular image could have been produced by a given model. The mean and standard deviation across the 100 shuffled patterns is shown on a log scale. The significantly higher deviances for the shuffled patterns and the original pattern demonstrate the non-random distribution of the cell types. How the extremely high deviances seen in some cases can be obtained is discussed in the Materials and methods.
Fig 2.
Performance comparison between multirange and single range multitype Strauss Hardcore models.
The average deviance per cell for all cells, real cells, and dummy cells are shown (error bars show 95% confidence limits). The radii are in pixels, and correspond to 38 to 188 microns.
Fig 3.
Comparison of cell type spatial relationships within and across different tissues.
(A) The interaction coefficients between models are directly compared using Gaussian kernel similarity. Lighter color indicates greater similarity. (B) The predictive accuracy on held-out images of a given tissue as well as images from other tissues was measured using wmAUC. In each tissue panel, the violin plots are arranged in descending order of the mean from left to right, and the mean is indicated by an “x”.
Fig 4.
Evaluating tissue heterogeneity of cell type relationships.
Panels A to E show the top 2 principal components of the interaction coefficients of various trained models for different tile sizes. Symbol colors are blue for 2500x2500 tiles, orange for 5000x5000 tiles, green for each original image, and red x’s for all original images combined. Panel F illustrates the change of heterogeneity with the tile size for the five tissues. Note that the PC1 and PC2 axis limits in panels A to C are ten times smaller than those in Panels D and E since there is much less variation in those tissues.
Fig 5.
Cell type interaction graph for five cell types across five different tissues.
The size of each node corresponds to the total strength of self-interaction across five distance ranges for that cell type (see S1 Fig for strength of self-interaction at each range). Each pair of nodes is interconnected by five arcs, each representing a different distance range. The range increases from left to right or from bottom to top, with the smallest and farthest ranges corresponding to the most curved arcs. The strength of the relationship between two cell types is depicted by the thickness of the arc, while the nature of their interaction is indicated by the color of the arc (blue as attraction and red as repulsion). (A) A direct, unfiltered illustration by raw interaction coefficients (B) Interaction coefficients adjusted by base intensities of corresponding cell types.
Fig 6.
A, B) Interaction graphs similar to Fig 5A are shown for all five ranges (A) and for just the first range (B). C) Heatmap showing the pairwise spatial interaction scores between endothelial cells, fibroblasts, and other cell types. Each cell displays the 90% trimmed mean interaction score (top) and the Winsorized standard error (bottom) within the first distance range across 59 images. Among all combinations, the fibroblast–endothelial cell pair exhibits the strongest positive spatial association, with relatively low variability across samples. D) Similar heatmap for self-interactions for all cell types. Fibroblasts and myeloid cells exhibit the strongest self-interaction. E) Scatter plot comparing interaction scores between myeloid cells and PD-1 negative or positive T cells for 59 images. F) Scatter plot of interaction scores between migratory dendritic cells (migDCs) and PD-1 negative or positive T cells. Only images with scores the range (–2, 2) on both axes are shown to highlight the overall trend.
Fig 7.
Real and synthetic tissue images across five tissue types.
Synthetic images were generated using method 2 (see Materials and methods). Each color represents a unique cell type, consistent with representations in other figures.