Flowchart of methodology.

(A) We collected bone marrow data from relapsing (R) and non-relapsing (NR) B-ALL patients at the time of diagnosis. (B) These samples were analysed via flow cytometry (FC) which gave rise to single-cell data with information on immunophenotypic (IPT) markers. (C) We pre-processed these data and selected the patients’ B lymphocytes. (D) Our aim was to obtain quantitative biomarkers from the IPT markers that can be used to identify patients at risk of relapse. (E) We conducted topological data analysis (TDA), which quantifies the shape of data via topological characteristics. (F) An important tool in TDA is persistent homology (PH), which can be used to obtain summaries in the form of persistence barcodes. Barcodes are topological signatures of the data and show topological features such as connected components and loops as well as their scale in the data. (G) Persistence barcodes can be transformed into vector summaries called persistence images. As a second approach, we used these images for classification.