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Topology across scales on heterogeneous cell data

Fig 7

PWDS and Betti curves for all cell types together in the human lung tissue.

A: Visualisation of PWDS for all cell types together with a choice of six representative samples out of 32. The visualisation corresponds to loops in PH alpha, with threshold parameters and . We observe the extensive cellular infiltrate in the lung tissue infected with COVID-19, indicated by small light-red triangles. In healthy samples PH detects the cavities in the lungs formed by thin walls of cells, indicated by intense red-triangles. For some COVID-19 samples, holes within the cellular infiltrate are also detected. Since there is not much noise inside the holes in this data set, there is a small number of blue triangles. Most of them correspond to either holes of concave shapes, or to holes whose walls are not completely contained in the sample, so they are formed by distal cells. B: All cells normalised Betti curves of degree 1 of the alpha filtration. We observe that diseased samples have a very similar behaviour to what we observed in the spleen data set, a peak in the small-scale due to the presence of large dense regions. The Betti-1 curves for the healthy samples do not have a pronounced peak at small scales, since the thin walls do not contain a large number of small-scale loops, but they have heavier tails due to the large proportion of large-scale holes.

doi: https://doi.org/10.1371/journal.pcbi.1013460.g007