# From LQ to AI-BED-Fx: A Unified Multi-Fraction Radiobiological and Machine-Learning Framework for Gamma Knife Radiosurgery Across Intracranial Pathologies

## TL;DR

This paper introduces a new framework combining radiobiology and machine learning to improve Gamma Knife radiosurgery planning for brain conditions.

## Contribution

AI-BED-Fx is the first unified multi-fraction radiobiological and machine-learning framework for Gamma Knife radiosurgery across various brain pathologies.

## Key findings

- AI-BED-Fx produced realistic BED distributions and biologically coherent dose–response relationships for four brain pathologies.
- Biological dose (BED) improved outcome prediction for some conditions like AVM and meningioma but not for others like brain metastases.
- A neural-network surrogate accurately reproduced radiobiological BED calculations with high fidelity.

## Abstract

Gamma Knife radiosurgery is a precise form of brain radiation treatment, but treatment decisions are still mostly based on physical dose measurements that do not reflect how living tissue responds to radiation over time, especially when treatment is given in multiple sessions. Existing biological models are mainly designed for single-session treatments and are not well suited for modern multi-session Gamma Knife approaches. In this study, we introduce a new biologically based framework that estimates how effective radiation is at damaging target tissue across one, three, or five treatment sessions. Using simulated disease-specific data and artificial intelligence methods, we show that biological dose information improves outcome prediction for some brain conditions but not for others. These results highlight when biological modeling is useful and provide a foundation for more personalized, biology-informed radiosurgery planning in future research and clinical practice.

Background: Gamma Knife radiosurgery (GKS) delivers highly conformal intracranial irradiation, yet clinical decision-making still relies predominantly on physical dose metrics that do not account for fractionation, dose rate, treatment time, or DNA repair. Classical radiobiological models—including the linear–quadratic (LQ) formula and the Jones–Hopewell single-session repair model—do not extend naturally to 3- and 5-fraction GKS. Meanwhile, growing evidence suggests that biologically effective dose (BED) may better capture radiosurgical response in selected pathologies. A unified, biologically grounded, multi-fraction GKS framework has been lacking. Methods: We developed AI-BED-Fx, the first multi-fraction extension of the Jones–Hopewell radiobiological model capable of computing fraction-resolved BED for 1-, 3-, and 5-fraction GKS. The framework incorporates α/β ratio, dual-component repair kinetics, isocentre geometry, beam-on–time structure, and lesion-specific biological parameters. Four synthetic pathology-specific cohorts—arteriovenous malformation (AVM), meningioma (MEN), vestibular schwannoma (VS), and brain metastasis (BM)—were generated using distinct radiobiological signatures. Machine-learning models were trained to quantify the predictive value of physical dose versus BED for local control or obliteration. Additional experiments included Bayesian estimation of α/β and a neural-network surrogate for fast BED prediction. An exploratory comparison with a 60-lesion clinical brain–metastasis dataset was performed to assess whether key trends observed in the synthetic BM cohort were consistent with real radiosurgical outcomes. Results: AI-BED-Fx produced realistic pathology-specific BED distributions (AVM 60–210 Gy2.47; MEN 41–85 Gy3.5; VS 46–68 Gy3; BM 37–75 Gy10) and biologically coherent dose–response relationships. Predictive modeling demonstrated strong pathology dependence. In AVM, the three models achieved AUCs of 0.921 (Model A), 0.922 (Model B), and 0.924 (Model C), with corresponding Brier scores of 0.054, 0.051, and 0.051, with BED-based models performing best. In meningioma, BED was the dominant predictor, with AUCs of 0.642 (Model A), 0.660 (Model B), and 0.661 (Model C) and Brier scores of 0.181, 0.177, and 0.179, respectively. In vestibular schwannoma, the narrow BED range resulted in minimal BED contribution, with AUCs of 0.812, 0.827, and 0.830 and Brier scores of 0.165, 0.160, and 0.162, with physical dose and tumor volume determining performance. In brain metastases, outcomes were driven primarily by volume and physical dose, with AUCs of 0.614, 0.630, and 0.629 and Brier scores of 0.254, 0.250, and 0.253, showing negligible improvement from BED. AI-BED-Fx also accurately recovered the true α/β from synthetic outcomes (posterior mean 2.54 vs. true 2.47), and a neural-network surrogate reproduced full radiobiological BED calculations with near-perfect fidelity (R2 = 0.9991). Conclusions: AI-BED-Fx provides the first unified, biologically explicit framework for modeling single- and multi-fraction Gamma Knife radiosurgery. The findings show that the predictive usefulness of BED is pathology-specific rather than universal, and that radiobiological dose provides additional predictive value only when repair kinetics and dose–response biology support it. By integrating mechanistic radiobiology with machine learning, AI-BED-Fx establishes the conceptual and computational foundations for biologically adaptive, AI-guided radiosurgery, and cross-pathology comparison of treatment response. This work uses large radiobiologically grounded synthetic cohorts for methodological validation; limited real-patient data are included only for exploratory consistency checks, and full clinical validation is planned.