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. 2024 Apr 8;14:8250. doi: 10.1038/s41598-024-58684-6

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© The Author(s) 2024

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Analyses of the maps of hidden units inside the LSTM-RNN model, which has 100 hidden units at each step and 18 steps in total. At each step, the tumor volume would be a linear combination of the values of 100 hidden units. The first time step on the horizontal axis corresponds to the day when the first anti-PD-L1 was administered. (a) Group 1 (isotype control) versus group 3 (20 Gy on day 3, isotype control). (b) Group 7 (20 Gy on day 3, 20 Gy on day 13, isotype control) vs. group 3. (c) Group 4 (20 Gy on day 3, anti-PD-L1) vs. group 3. (d) Group 8 (20 Gy on day 3, 20 Gy on day 13, anti-PD-L1) vs. group 7. We hypothesize that the difference between two groups, reveals the unique therapeutic effect attributable to either anti-PD-L1 or radiation. Three highlighted regions (vertical index: 1–5, 20–45, 85–90) correspond to radiation, while the fourth highlighted region (vertical index: 65–75, bold boundaries) corresponds to anti-PD-L1.