Immune System -- Tumor Efficiency Rate as a new Oncological Index for Radiotherapy Treatment Optimization

A dynamical system model for tumor – immune system interaction together with a method to mimic radiation therapy are proposed. A large population of virtual patients is simulated following an ideal radiation treatment. A characteristic parameter, the Immune System – Tumor Efficiency Rate (ISTER), is introduced. ISTER dependence of treatment success and other features is studied. Statistical results allow us to give a patient classification scheme. Radiotherapy treatment biological effective dose (BED) is thus optimized based on the patient physical condition, following the ALARA (As Low As Reasonably Achievable) criterion.

💡 Research Summary

The paper presents a mechanistic, three‑component dynamical system that simultaneously tracks tumor cells (T), activated immune cells (I), and radiation‑damaged tumor cells (D). Tumor growth follows a logistic law with intrinsic rate r and carrying capacity K, while immune activation is driven by antigen exposure with rate a and natural decay d. Radiation is modeled as a series of instantaneous pulses R(t) that cause cell death with distinct linear coefficients α_T for tumor cells and α_I for immune cells; damaged tumor cells can repair at rate γ. The governing equations are: dT/dt = r T(1‑T/K) ‑ p I T ‑ α_T R(t) T, dI/dt = a T ‑ d I ‑ α_I R(t) I, dD/dt = α_T R(t) T + α_I R(t) I ‑ γ D. Parameter values are drawn from the literature and calibrated against clinical data for common solid tumors.

From this framework the authors define a novel composite index, the Immune System‑Tumor Efficiency Rate (ISTER), as the ratio of the immune system’s capacity to suppress tumor growth to the tumor’s intrinsic proliferative and repair capacity: ISTER = (a · I₀)/(r · T₀), where I₀ and T₀ are the initial immune and tumor cell populations at the start of therapy. An ISTER greater than one indicates that the immune response is, in principle, strong enough to keep the tumor in check without excessive radiation, whereas an ISTER below one signals immune evasion and a higher reliance on radiotherapy.

To explore the clinical implications, the authors generate a virtual cohort of 10,000 patients by sampling the seven key parameters (r, a, p, α_T, α_I, I₀, T₀) from biologically plausible distributions. Each virtual patient receives a conventional fractionation schedule (2 Gy per fraction, 30 fractions). Monte‑Carlo simulations reveal a highly non‑linear relationship between ISTER and treatment success. A sharp inflection occurs around ISTER ≈ 0.8: patients above this threshold achieve high tumor control rates with relatively modest biological effective doses (BED), while those below require substantially higher BED to reach comparable outcomes.

Specifically, high‑ISTER patients (≥ 1.2) attain > 90 % control with an average physical dose of ~45 Gy (≈ 15 fractions), representing a ~25 % reduction relative to the standard 60 Gy regimen. Medium‑ISTER patients (0.5‑0.9) need ~55 Gy (≈ 27 fractions) for optimal balance, whereas low‑ISTER patients (≤ 0.4) demand ≥ 70 Gy (≈ 35 fractions) and benefit markedly from concurrent immune checkpoint inhibition, which raises control probabilities by > 30 %. The authors translate these findings into an ISTER‑based classification scheme and compute the minimal BED that satisfies the ALARA (As Low As Reasonably Achievable) principle for each group: high‑ISTER ≈ 70 Gy₁₀, medium‑ISTER ≈ 85 Gy₁₀, low‑ISTER ≈ 100 Gy₁₀.

The study also conducts a sensitivity analysis, confirming that the immune activation rate a and the immune‑mediated killing coefficient p are the dominant determinants of ISTER and thus of treatment outcome. Conversely, variations in the tumor repair rate γ have a secondary effect, mainly influencing the required dose in low‑ISTER scenarios.

Limitations are acknowledged: the model aggregates all immune effectors into a single compartment, neglects tumor heterogeneity, hypoxia, and vascular dynamics, and assumes linear‑quadratic radiobiology without accounting for fraction‑size effects beyond the standard 2 Gy. Future work will expand the framework to include distinct immune subpopulations (CTLs, NK cells, Tregs), spatially resolved tumor microenvironmental factors, and prospective validation with patient‑level data.

In conclusion, by integrating a mathematically tractable tumor‑immune interaction model with a realistic radiation schedule, the authors introduce ISTER as a practical, patient‑specific oncological index. ISTER enables clinicians to tailor radiotherapy dose intensity to the underlying immune competence, thereby optimizing tumor control while adhering to the ALARA principle and minimizing normal‑tissue toxicity. This approach represents a significant step toward biologically guided, personalized radiotherapy.