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. 2023 Jul 6;13(1):10981.
doi: 10.1038/s41598-023-38232-4.

Mathematical model combined with microdosimetric kinetic model for tumor volume calculation in stereotactic body radiation therapy

Hisashi Nakano  1   2 , Takehiro Shiinoki  3 , Satoshi Tanabe  4 , Satoru Utsunomiya  5 , Takeshi Takizawa  6   7 , Motoki Kaidu  7 , Teiji Nishio  8 , Hiroyuki Ishikawa  7
Affiliations

Mathematical model combined with microdosimetric kinetic model for tumor volume calculation in stereotactic body radiation therapy

Hisashi Nakano et al. Sci Rep. .

Abstract

We proposed a new mathematical model that combines an ordinary differential equation (ODE) and microdosimetric kinetic model (MKM) to predict the tumor-cell lethal effect of Stereotactic body radiation therapy (SBRT) applied to non-small cell lung cancer (NSCLC). The tumor growth volume was calculated by the ODE in the multi-component mathematical model (MCM) for the cell lines NSCLC A549 and NCI-H460 (H460). The prescription doses 48 Gy/4 fr and 54 Gy/3 fr were used in the SBRT, and the effect of the SBRT on tumor cells was evaluated by the MKM. We also evaluated the effects of (1) linear quadratic model (LQM) and the MKM, (2) varying the ratio of active and quiescent tumors for the total tumor volume, and (3) the length of the dose-delivery time per fractionated dose (tinter) on the initial tumor volume. We used the ratio of the tumor volume at 1 day after the end of irradiation to the tumor volume before irradiation to define the radiation effectiveness value (REV). The combination of MKM and MCM significantly reduced REV at 48 Gy/4 fr compared to the combination of LQM and MCM. The ratio of active tumors and the prolonging of tinter affected the decrease in the REV for A549 and H460 cells. We evaluated the tumor volume considering a large fractionated dose and the dose-delivery time by combining the MKM with a mathematical model of tumor growth using an ODE in lung SBRT for NSCLC A549 and H460 cells.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
The effect of radiotherapy on tumor volume calculations combining the multicomponent mathematical model (MCM) (lower compartment) representing tumor growth and microdosimetric kinetic model (MKM) (upper compartment) to assess tumor survival.
Figure 2
Figure 2
Comparison of the tumor growth volume measurements of A549 (left) and H460 (right) NSCLC cells with the values calculated by the MCM.
Figure 3
Figure 3
The surviving fraction (SF) values calculated by the LQM and the MKM models compared to the measured values, presented for A549 (left) and H460 (right).
Figure 4
Figure 4
(a) Effect on each initial tumor volume (500, 1000, 2000 cm3) in 48 Gy/4 fr irradiation of A549 and H460 non-small cell lung cancer cells (left two columns). (b) Effect on each initial tumor volume (500, 1000, 2000 cm3) in 54 Gy/3 fr irradiation of A549 and H460 cells (right two columns).
Figure 5
Figure 5
Effect of varying the V1 and V2 ratio for total tumor volume on the REVs in 48 Gy/4 fr irradiation of A549 and H460 non-small cell lung cancer (NSCLC) cells.
Figure 6
Figure 6
Effect of varying the V1 and V2 ratio on the REVs in 54 Gy/3 fr irradiation of A549 and H460 NSCLC cells.
Figure 7
Figure 7
(a) Effect of the VQ ratio on the total tumor volume in 48 Gy/4 fr irradiation of A549 and H460 non-small cell lung cancer cells (left two columns). (b) Effect of the VQ ratio on the total tumor volume in 54 Gy/3 fr irradiation of A549 and H460 cells (right two columns).
Figure 8
Figure 8
(a) Effect of the dose delivery time tintra on the REVs in 48 Gy/4 fr irradiation of A549 and H460 non-small cell lung cancer cells (left two columns). (b) The influence of the dose delivery time tintra on the REVs in 54 Gy/3 fr irradiation of A549 and H460 cells (right two columns).
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