Resilience-depletion hypothesis: Unifying BED from conventional to ablative radiotherapy

Cell-survival modeling remains fundamental to radiobiology because it underlies both mechanistic interpretation of radiosensitivity and practical isoeffect quantities such as the biologically effective dose (BED). The linear-quadratic (LQ) model remains the standard low-dose framework, yet its direct extrapolation to the large doses per fraction used in stereotactic body radiotherapy (SBRT) is problematic. Piecewise corrections such as the universal survival curve (USC) recover the expected high-dose tail by explicit stitching, but no single continuous formalism has achieved broad acceptance across the therapeutic range while also providing a clear language for heterogeneous survival-curve phenotypes.

To present the resilience-depletion (RD) framework as a macroscopic theory of acute cell survival under stress, and to develop from it a unified BED formalism with direct clinical applicability in radiotherapy.

Starting from a single postulate for passive cells under acute exposure, we derive a continuous hazard-based survival law in which cumulative stress progressively depletes a resilience reserve. The framework is formulated in generalized homogeneous and heterogeneous forms, its limiting behaviors are analyzed, and exact algebraic mappings from the historical descriptors $(\alpha /\beta ,D_q,D_0)$ to RD parameters are obtained. Over the therapeutic range, the generalized law reduces to an effective three-parameter form from which unified BED, EQD2, and exact isoeffect inversions follow. The reduced model is then examined against curated clonogenic datasets and through back-projection of accepted NSCLC hypofractionated regimens to a conventional reference scale.

RD yields a continuous cumulative hazard governed in its therapeutic form by three macroscopic parameters: initial resilience ( $r$ ), sensitization rate ( $s$ ), and killing efficiency ( $k$ ). In the homogeneous single-target limit, the low-dose expansion recovers LQ behavior, whereas the high-dose limit approaches the expected shifted linear tail without piecewise construction. The generalized formulation further shows how homogeneous multi-target structure produces extended initial near-linearity and how heterogeneous mixtures generate inverse-shoulder ensemble behavior, including compact treatment-range representations with effective . Under acute irradiation, the therapeutic single-target law is mathematically equivalent to the acute Linear Quadratic-Linear (LQ-L) class after reparameterization. Clinically, the resulting BED framework provides exact schedule inversion and maps accepted NSCLC regimens to a comparatively coherent EQD2 neighborhood around the conventional $60\mathrm{Gy}$  reference.

RD provides a continuous macroscopic theory of acute radiation survival that unifies low-dose LQ structure, high-dose linear-tail behavior, and key homogeneous and heterogeneous survival-curve topologies within a single hazard-based formalism. In this sense, it is not only a replacement BED expression, but a broader statistical framework linking observed survival geometry to underlying effective structure. Its reduced therapeutic form retains immediate clinical utility through unified BED, EQD2, exact isoeffect inversion, and direct translation from historical radiobiological descriptors. These results support RD as a consistent acute baseline for both radiobiological interpretation and practical radiotherapy modeling. Extension to dose-rate effects, incomplete recovery, brachytherapy, and other prolonged-delivery settings will require explicit time-dependent recovery kinetics beyond the present acute formulation.