Fig. 3: Analysis of HCC data with spatial transcriptomics (n = 9, 812 spots).

a First and third rows: H& E images and manual annotations by a pathologist of tumor and tumor-adjacent tissue sections. Second and fourth rows: estimated latent time heatmap for SDEvelo and scVelo (dyn). SDEvelo identified clear gradual latent time transitions from stroma to TNE, while scVelo failed to obtain a clear and correct pattern that matched the annotations. b PCA-projected streamline plots for four human HCC samples. Clusters 1-5 represent TNE regions and clusters 6–9 are stromal regions. c Boxplots of cross-boundary direction correctness (CBDir) and AUC used to compare SDEvelo with other methods (n = 4 HCC sections biological replicates). Higher CBDir and AUC indicate better performance in terms of velocity estimates more consistent with the biological transitions. In the boxplot, the center line, box lines and whiskers represent the median, upper, and lower quartiles, and 1.5 times interquartile range, respectively. Source data are provided as a Source Data file. d Heatmaps of rank correlation across four HCC sections to benchmark the performance of all methods. A higher Spearman rank correlation suggests that the estimated latent time is more consistent with the true transitions. Source data are provided as a Source Data file. e Estimated latent time heatmap for SDEvelo in tumor-adjacent tissue sections, with spots whose latent time values are between 0.275 and 0.325 highlighted. The highlighted spots delineate a clear boundary between the stromal and TNE regions. f PPI network among TTR, APOC1, APOA1, APOE, APOC3, and C3, in which the connections represent significant interactions between the corresponding proteins.