Optimal transport analysis of high-dimensional flow cytometry data in immuno-oncology

Advances in single-cell and spatial profiling have enabled detailed characterization of heterogeneous samples, but analyzing this data remains challenging in settings involving multiple comparisons. While tools like UMAP and t-SNE are valuable for visualization, their stochastic, parameter-sensitive nature limits their use in longitudinal comparisons, treatment group analysis, and multicenter trials. Although OT was first described in the 19th century, the Sinkhorn algorithm makes it computationally tractable for high-dimensional data. By directly comparing distributions of cellular states, OT provides reproducible measures of change in high-dimensional space. This framework is amenable to integration with machine learning, including deep generative models.

OT was applied to longitudinal data from a phase I trial of tocilizumab for cavitary malignancies (NCT06016179). The current implementation makes use of expert-guided phenotypic population definitions and their relationships. An OT-based graph representation was created for baseline and follow-up samples. The graph layout was fixed across samples and computed from phenotypic relationships. In this implementation vertex radii are proportional to their relative abundance, allowing for rapid visual assessment of population-level increases and decreases. Graph edge thickness and color encode inter-population similarity based on the optimal transport (Sinkhorn) distance between marker expression distributions.

This representation enabled rapid identification of populations undergoing substantial change, such as the CD8+/IFNɣ+ population, which decreased from 63% to 17% of CD8+ T cells following treatment. Population changes across all fluorescence parameters were encoded in the graph edit distance (GED), which captures changes in population abundance and phenotypic shifts in marker space.

Future implementations can combine this expert-guided approach with unbiased clustering algorithms to enhance scalability and cross-platform harmonization. In our recently initiated clinical trials, we will apply OT to identify key shifts in tumor, immune, and stromal cell states, summarizing patient trajectories and quantitatively supporting predictive models of treatment response. Potential applications include quantifying residual disease after chemotherapy, tracking immune activation during immunotherapy, and linking host-microbiome interactions to disease progression. This approach overcomes the limitations of traditional, local-structure-optimized tools (UMAP or t-SNE) to provide a comprehensive, longitudinal view of tumor evolution and treatment response.