Fig. 6. Topological descriptors extracted from tumor blood vessel networks treated with radiation therapy.

We normalized all descriptors with respect to values on the day on which treatment is administered (day 0) or, for controls, the day on which observations commenced (day 0). Data were collected from control mice (beige), mice treated with fractionated irradiation (FIR; brown), and mice treated with single-dose irradiation (IR; blue). (i) Tortuosity was computed as the ratio of short bars (≤10% of maximal radius used in the radial filtration) in the dimension 0 barcodes of the radial filtration to the number of vessel segments. (ii) Loops are the number of bars in the dimension 1 barcodes of the radial filtration per vessel segment in the network. (iii) Spatiotemporal resolution of the number of loops per vessel segment. We illustrate the changes in the median number of loops (normalized by day 0) in different radial intervals around the tumor centers over the days of observation. The yellow arrows highlight days for which the tumors have received treatment on the prior day [i.e., an arrow on day 1 signifies that (a dose of) treatment was administered on day 0].