Density-based reconstruction of anatomical structures

In sosta, reconstruction of the outlines of anatomical structures is performed by using a cut-off on a point pattern density estimate, where the point pattern corresponds to either the centroids of selected cell type(s), the locations of transcripts of interest, features marking a spatial domain (or cluster or functional pathway), or any other spatial covariate associated with individual cells. As previously described by Diggle et al. [11], a density image of a point pattern can be estimated by

(1)

where is the estimated intensity at point u, is a Gaussian kernel and e(u) is an edge correction factor.

By default, the bandwidth of the smoothing kernel is estimated using cross validation on the bandwidth selection as described by Diggle et al. [11]. The density estimation and kernel selection are implemented in the R package spatstat [12]. To facilitate the use of this approach, we implemented our package within the R/Bioconductor environment and work with common data structures for spatial (omics) data. The resulting anatomical structures are stored as polygons using the sf package [13].

Parameter estimation

To estimate the cut-off threshold value c for reconstruction, we use an automated estimation of the threshold where m₁ and m₂ are the density values at the first and second mode of the intensity distribution over all pixels in the estimated density image. In settings where the distribution is unimodal, the cut-off value lies at the peak of the distribution. We further provide auxiliary functions to facilitate manual adjustment and optimization of this cut-off value, as well as the bandwidth of the Gaussian kernel k. In particular, we provide functions to visualise density images, the intensity distributions, and to estimate the range and variability of automatically estimated parameters. Overall, we noticed that downstream results were consistent across a range of parameter settings (i.e., bandwidth of smoothing kernel and cut-off threshold), indicating robustness of our reconstruction approach. However, at an upper or lower range of values we observed substantial deviations, especially in the number of detected structures (Fig C.C in S1 File).

Quantification of morphological features

After the anatomical structures have been reconstructed, sosta offers functions to calculate a range of geometric features such as the area, circularity or eccentricity of each individual structure. An overview of all structural metrics calculated by sosta given in Table A in S1 File.

Cell-based features

In addition to morphological features, sosta offers functions that relate individual cells to anatomical structures. They compute intersections between cells and structures and measure distances to structure borders. The functions support quantifying cell type composition dynamics and defining gradients relative to structure border or anatomical landmarks.

Differential feature analysis

Multi-sample multi-condition analysis of spatial omics datasets requires care as this type of data often harbours multiple levels of correlation. In the case of structure-based analysis, we can have multiple relevant experimental units such as multiple structures in a section, multiple sections in one slide, multiple slides per patient and multiple patients per condition. In downstream analysis, it is critical to recognize that these are not independent experimental units. For differential feature analysis, linear mixed effects modelling tools offer effective strategies to account for nested correlation structure [14]. An analysis of a multi-sample multi-condition spatial proteomics dataset by Damond et al. [15] revealed strong correlation effects within experimental units at different levels. Furthermore, using a semi-synthetic simulation framework adapted from Yu et al. [14] we noticed that failing to account for the nested correlation structure in the Damond et al. dataset lead to an increase of the false discovery rate (FDR) of up to 20% while mixed effect models retained the FDR below the selected 5% level (Fig A and Suppl. Methods in S1 File).

Methods comparison

Other methods exist that take coordinates and labels as input and output a polygon that can be used for downstream morphological quantification and subsequent geometric operations. We compared sosta against the R/Bioconductor packages imcRtools [16] and SPIAT [17], and the Python package CellCharter [5] that use a concave hull around a defined set of points to define structures and to the Python package GRIDGENE [6] that employs a point pattern density-based approach conceptually similar to ours (Suppl. Methods in S1 File). We adapted the code of SPIAT as it did not include any function that outputs polygons but only calculates them internally. Among these methods, GRIDGENE does not include automatic estimation of parameters for structure reconstruction so that all parameters require manual adjustment.

Since ground truth datasets with expert annotations often exhibit subjective annotation bias [8], we based our comparison on simulations. We simulated binary images using random seeds and a Gaussian smoothing kernel to define structures and subsequently sampled points within these structures using a Poisson process with varying intensity, including background noise with varying strength. We then performed reconstruction using the different methods and converted the resulting polygons into binary images. Method performance was evaluated using the Jaccard index between the original binary image and the reconstruction (Fig B and Suppl. Methods in S1 File).

Density based methods clearly outperformed approaches that construct a concave hull around a set of points. sosta achieved the best performance, with GRIDGENE reaching similar results. However, this occurred only when selecting the best GRIDGENE result across a range of parameters, using the highest Jaccard index against the ground truth. The performance of sosta showed a substantially higher variance in high noise settings compared to low noise settings, but the average performance was comparable in both settings. The number of target cells had little influence on the reconstruction accuracy. Overall, these results highlight the advantage of density-based methods and automated parameters selection as implemented in sosta (Fig B.C-B.E in S1 File).

Reconstruction and quantification of epithelial crypts in colon tissue

To highlight structure-based analysis of spatial transcriptomics data, we first quantified structural changes in the transformation from healthy human colon (HC) tissue to colorectal cancer (CRC) [10] (Figs 2A and C.A-C.C in S1 File). This transition from HC crypt epithelial cells to CRC is a process that includes intermediate stages, such as polyps or tubulovillous adenomas (TVAs). These stages are typically identified by histopathology since they are characterized by discernible cellular morphology and structural rearrangement. The transcriptional dynamics along this transition have been studied in Crowell et al. [10].

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Fig 2. Two examples of structure-based analysis of spatial transcriptomics data.

A) Overview of section 110 from Crowell et al. [10] (REF = reference / healthy colon, TVA = TVA regions, CRC = colorectal cancer regions). B) Subregion indicated by the dotted box in A, rotated counter-clockwise by 90°, that reflects the transition between normal colonic crypts and premalignant TVA regions. Results of the sosta density-based reconstruction are randomly coloured to highlight unique structures. C) Epithelial structures in B coloured by their respective fibre width. D) Boxplot of the distribution of fibre width per cell (each cell was assigned the fibre width metric of its corresponding epithelial structure) grouped by the assigned region. E) Boxplot of per-cell fibre widths grouped by cell types. x-axis ordered by median fibre width. F) Association between the median fibre width per epithelial structure and its median (inferred) pseudo-time [10]. G) Reconstructed epithelial crypts of B. The colour reflects their corresponding “shape index”. H) Association between the median pseudo-time and the median shape index per reconstructed epithelial crypt. I) Examples of a de novo identified transition crypts using structure-based analysis and J) corresponding histopathology image (adjacent section, adapted from [10]). K) Structure-based analysis of germinal centres (GCs) in the human tonsil [20]; black outlines correspond to reconstructed GCs, colours reflect inferred clusters. Coloured squares correspond to reference points used to reconstruct anatomical reference axes (white lines). L) Reference axes through GCs; colours correspond to distances scaled between 0 and 1 within each GC. M) Heatmap of 1569 genes with spatially-varying expression within the GCs. Highlighted are known marker genes. LZ = light zone, DZ = dark zone. J was adapted from [30]; licensed under CC-BY 4.0.

https://doi.org/10.1371/journal.pcbi.1014551.g002

To accentuate morphological changes between HC and (pre-)malignant regions, we calculated a range of geometric features using sosta and centred on a geometric metric called “fibre width”, which represents the width of the between inner and outer crypt border (Fig 1C and Table A in S1 File). Fibre width increased along the pathological progression from HC to TVA to CRC, both at the structure and cell type level (Fig 2D-2E). As such, this metric reflects the gradual morphological changes related to increase in crypt thickness. In healthy tissue, epithelial cells are lining the crypt; in hypertrophy and hyperplasia, there is an increase in size and number of epithelial cells, respectively. Next, dysplasia denotes a known premalignant state in which epithelial cells lose differentiation, present abnormal size and shape and lack polarization followed by carcinoma [18,19]. To further study this progression, we compared the association of fibre width with the median pseudo-time per structure as inferred in the original publication for each cell. We observed a strong positive correlation between the median fibre width per epithelial structure and the median pseudo-time of cells within the structure (Spearmans’s = 0.46, p-value < 10⁻¹⁰, Fig 2F). In addition to structural analysis of the epithelial cell layer, we further reconstructed and quantified individual epithelial crypts (Fig 2G). We found that the “shape index”, a morphological measure of a shape’s regularity, reflects the transition from regular crypts in the normal epithelium to irregular ones in premalignant regions (Spearmans’s = 0.22, p-value < 10⁻¹⁰, Fig 2H). Furthermore, we used the reconstructed crypts to identify local transitions between normal and premalignant tissue, i.e., transition crypts. By filtering based on the frequency of cell types adjacent to the reconstructed crypts, we recovered one of seven manually annotated transition crypts and identified potentially de novo transition crypts. Although this approach failed to detect several manually annotated crypts, it revealed additional candidate crypts that also showed transition patterns in the histopathology image (Figs 2I-2J and C.D-C.H in S1 File, Suppl. Methods in S1 File).

By using structure-based analysis, we gained additional insight about the morphological transition during the progression to CRC. For illustration, this was done on a single slide. However, this type of analysis could also be performed with multiple replicates and across conditions. In this case, it is crucial to account for correlation of the repeated measurements (i.e., structures) on the same experimental unit (i.e., sample) (Fig 1C).

Reconstruction and analysis of anatomically relevant gradients in germinal centres of the human tonsil

In addition to geometric features, anatomical structures offer a baseline for structure-aware analysis of gene expression. Unlike conventional spatially variable gene analysis, this approach relates spatial variation of gene expression to meaningful anatomical axes. To demonstrate this, we performed structure-based analysis of a spatial transcriptomics dataset of human tonsil tissue [20] (Figs 2K and D in S1 File). Relevant anatomical structures in this dataset are germinal centres (GCs), locations where B cells mature along a defined anatomical trajectory: from light to dark zone (L/DZ) [21]. We used our density-based reconstruction approach to define GCs and, within each GC, constructed anatomically relevant axes by first identifying anatomical zonations in each GC then projecting a matching axis through each GC (Figs 2L and D in S1 File, Suppl. Methods). This allowed for quantification of gene expression along a unified anatomically relevant gradient across GCs.

Next, we averaged expression of all GC spots within binned distances and used the maximal information coefficient (MIC) [22], a metric that can capture linear and non-linear relationships, to identify genes that showed gene expression changes along the LZ-DZ axis. We identified a total of 1569 genes that showed a spatially varying gene expression profile (MIC > 0.999). These included known markers of B cells proliferation, maturation, and antigen presentation (e.g., MKI67, CIITA) [21,23] (Fig 2M).

In this example, structure-based analysis offered a straightforward approach to recover interpretable and anatomically relevant gene expression gradients without relying on discrete cell types.