The Biologically Effective Particle Number Ratio (BPNR): a new framework to quantify the therapeutic window in SFRT and other modalities

TL;DR

The paper introduces BPNR, a new outcome-based framework that quantifies therapeutic window changes in radiation therapy modalities using measurable particle numbers, avoiding ambiguous dose metrics.

Contribution

It presents BPNR as a novel, model-independent metric for comparing therapeutic windows across different radiation therapy modalities based on biological outcomes.

Findings

BPNR provides a clear measure of therapeutic window changes.

Application to proton minibeam radiotherapy shows RBPNR > 1.4.

Framework is modality-agnostic and applicable to various therapies.

Abstract

Spatially Fractionated Radiation Therapy (SFRT) produces highly heterogeneous dose distributions, for which conventional metrics such as peak, valley, or average dose can yield ambiguous or inconsistent estimates of therapeutic window changes. These dose descriptors are not uniquely linked to biological outcome, complicating comparisons between modalities. We introduce the Biologically Effective Particle Number Ratio (BPNR), a model-independent and outcome-based framework that quantifies therapeutic window changes using directly measurable delivery quantities rather than spatial dose metrics. BPNR is defined as the ratio of total particle numbers (proportional to monitor units, MU) required to reach specified levels of tumor control probability (TCP) and normal tissue complication probability (NTCP). The relative BPNR (RBPNR) compares therapeutic windows across modalities and avoids ambiguities of spatial dose averaging by relying solely on biological endpoints. As an illustration, we apply the framework to preclinical proton minibeam radiotherapy (pMBRT) versus conventional proton therapy. The absence of normal tissue complications at the highest tested MU in the pMBRT arm yields an RBPNR > 1.4, indicating a widened therapeutic window. The BPNR/RBPNR methodology provides a concise, experimentally grounded, and modality-agnostic way to quantify therapeutic window changes, with potential applications across SFRT, FLASH, high-LET radiation, and combination therapies.