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Low dimensional representation of multi-patient flow cytometry datasets using optimal transport for minimal residual disease detection in leukemia

Erell Gachon, Jérémie Bigot, Elsa Cazelles, Audrey Bidet, Jean-Philippe Vial, Pierre-Yves Dumas, Aguirre Mimoun

TL;DR

This work tackles MRD detection in AML by recasting multi-patient flow cytometry datasets as high-dimensional probability measures and applying optimal-transport-based dimensionality reduction. By combining mean-measure quantization (via K-means on the merged data) with embeddings in linear spaces through either Wasserstein PCA or log-ratio PCA, the authors obtain informative 2D representations that reveal intra- and inter-patient variability and correlate with MRD measures. Across two datasets (DATAML-Bordeaux and HIPC), the OT-based approach outperforms kernel mean embeddings and aligns well with FlowSOM MRD results, enabling effective clustering and supervised classification of MRD status. This OT-driven framework offers a scalable, interpretable tool for MRD assessment and could enhance relapse prognosis when used alongside FlowSOM in clinical workflows.

Abstract

Representing and quantifying Minimal Residual Disease (MRD) in Acute Myeloid Leukemia (AML), a type of cancer that affects the blood and bone marrow, is essential in the prognosis and follow-up of AML patients. As traditional cytological analysis cannot detect leukemia cells below 5\%, the analysis of flow cytometry dataset is expected to provide more reliable results. In this paper, we explore statistical learning methods based on optimal transport (OT) to achieve a relevant low-dimensional representation of multi-patient flow cytometry measurements (FCM) datasets considered as high-dimensional probability distributions. Using the framework of OT, we justify the use of the K-means algorithm for dimensionality reduction of multiple large-scale point clouds through mean measure quantization by merging all the data into a single point cloud. After this quantization step, the visualization of the intra and inter-patients FCM variability is carried out by embedding low-dimensional quantized probability measures into a linear space using either Wasserstein Principal Component Analysis (PCA) through linearized OT or log-ratio PCA of compositional data. Using a publicly available FCM dataset and a FCM dataset from Bordeaux University Hospital, we demonstrate the benefits of our approach over the popular kernel mean embedding technique for statistical learning from multiple high-dimensional probability distributions. We also highlight the usefulness of our methodology for low-dimensional projection and clustering patient measurements according to their level of MRD in AML from FCM. In particular, our OT-based approach allows a relevant and informative two-dimensional representation of the results of the FlowSom algorithm, a state-of-the-art method for the detection of MRD in AML using multi-patient FCM.

Low dimensional representation of multi-patient flow cytometry datasets using optimal transport for minimal residual disease detection in leukemia

TL;DR

This work tackles MRD detection in AML by recasting multi-patient flow cytometry datasets as high-dimensional probability measures and applying optimal-transport-based dimensionality reduction. By combining mean-measure quantization (via K-means on the merged data) with embeddings in linear spaces through either Wasserstein PCA or log-ratio PCA, the authors obtain informative 2D representations that reveal intra- and inter-patient variability and correlate with MRD measures. Across two datasets (DATAML-Bordeaux and HIPC), the OT-based approach outperforms kernel mean embeddings and aligns well with FlowSOM MRD results, enabling effective clustering and supervised classification of MRD status. This OT-driven framework offers a scalable, interpretable tool for MRD assessment and could enhance relapse prognosis when used alongside FlowSOM in clinical workflows.

Abstract

Representing and quantifying Minimal Residual Disease (MRD) in Acute Myeloid Leukemia (AML), a type of cancer that affects the blood and bone marrow, is essential in the prognosis and follow-up of AML patients. As traditional cytological analysis cannot detect leukemia cells below 5\%, the analysis of flow cytometry dataset is expected to provide more reliable results. In this paper, we explore statistical learning methods based on optimal transport (OT) to achieve a relevant low-dimensional representation of multi-patient flow cytometry measurements (FCM) datasets considered as high-dimensional probability distributions. Using the framework of OT, we justify the use of the K-means algorithm for dimensionality reduction of multiple large-scale point clouds through mean measure quantization by merging all the data into a single point cloud. After this quantization step, the visualization of the intra and inter-patients FCM variability is carried out by embedding low-dimensional quantized probability measures into a linear space using either Wasserstein Principal Component Analysis (PCA) through linearized OT or log-ratio PCA of compositional data. Using a publicly available FCM dataset and a FCM dataset from Bordeaux University Hospital, we demonstrate the benefits of our approach over the popular kernel mean embedding technique for statistical learning from multiple high-dimensional probability distributions. We also highlight the usefulness of our methodology for low-dimensional projection and clustering patient measurements according to their level of MRD in AML from FCM. In particular, our OT-based approach allows a relevant and informative two-dimensional representation of the results of the FlowSom algorithm, a state-of-the-art method for the detection of MRD in AML using multi-patient FCM.
Paper Structure (28 sections, 1 theorem, 20 equations, 8 figures, 2 tables)

This paper contains 28 sections, 1 theorem, 20 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Contributions
  3. Outline of the Paper
  4. Materials and Methods
  5. DATAML-Bordeaux Study
  6. HIPC dataset
  7. The FlowSOM Method
  8. Optimal Transport
  9. Optimal Transport and Wasserstein Barycenter
  10. Dimension Reduction via Mean Measure Quantization
  11. An Embedding with the OT Linearization
  12. Representation of Datasets with PCA
  13. Statistical Analysis on the K-means Weight Vectors
  14. Statistical Analysis with Linearized OT
  15. Performance Evaluation
  16. ...and 13 more sections

Key Result

Proposition 1

When the $\mu^i$'s are absolutely continuous w.r.t. the Lebesgue measure, the Wasserstein barycenter problem with varying weights newbary is equivalent to the $K$-means quantization of the mean measure $\overline{\mu} = \frac{1}{N} \sum_{i=1}^N \mu^i$, that is, where $\overline{\mu} = \frac{1}{N} \sum_{i=1}^N \mu^i$ is the average measure, and $V_{x_k}$ is the Voronoi cell centered at point $x_k$

Figures (8)

  • Figure 1: HIPC dataset : Silhouette score and execution time of our method as a function of the number of clusters. The red dotted line represents the execution time for the reference measure chosen as either uniform, random among the $\nu^{i}$'s or the concatenation of two measures $(\nu^{i},\nu^{j})$.
  • Figure 2: Two-dimensional representations of the HIPC data using PCA on different embeddings : (top left) KME, (top right) K-Means + comp, (bottom left) K-Means + LinW2, (bottom right) FlowSOM + LinW2. Each color corresponds to a patient. Each marker encodes the laboratory where the data was processed.
  • Figure 3: Comparison of time of execution for the different embeddings.
  • Figure 4: Minimum Spanning Tree for the diagnosis and two follow-up measurements of one patient of the DATAML-Bordeaux dataset, and one normal bone marrow.
  • Figure 5: Two-dimensional representations of the DATAML-Bordeaux datasets using PCA on different embeddings : (top) K-Means + LinW2, (middle) K-Means + comp, (bottom) KME. Each dot represents a FCM sample. The colors encore the nature of the data : (red) diagnostic, (purple) normal bone marrow, (yellow) positive follow-up, (green) negative follow-up, (gray) no information on the MRD-BioM.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Proposition 1
  • proof : Proof of Proposition \ref{['prop1']}.