Effect of the dose distribution and organ architecture on the toxicity in FLASH radiotherapy: a modeling study

Abstract: Objective: This study aims to investigate the influence of organ architecture (specifically the distinction between serial and parallel tissue) on the protective FLASH effect when organs are irradiated with inhomogeneous dose distributions. Approach: An in silico modeling framework was developed using two distinct methods to calculate the effective FLASH dose: the first method utilized a biophysical model of radiolytic oxygen depletion (ROD); the second employed a phenomenological logistic function where the effective FLASH dose is a function of local dose and dose rate. Both models assume that the underlying mechanism behind the FLASH effect is local. Normal Tissue Complication Probability (NTCP) for heterogeneous dose distributions was calculated using the Lyman-Kutcher-Burman (LKB) model and the generalized equivalent uniform dose, varying the volume effect parameter n from 1.0 (parallel) to below 0.01 (serial) to explore different architectures. Results: Both the ROD and phenomenological models showed FLASH sparing compared to conventional radiotherapy. Also, the sparing increased with decreasing $n$ (the sparing is more important for serial organs). For example, for a specific calculation, when the NTCP for conventional radiotherapy was 0.2 (set value) the corresponding NTCP for FLASH delivery ranged from 0.14 for n=1 to 0.11 for n=0.1. Significance: Our results indicate that if the underlying mechanism/s behind the FLASH effect is/are local, the toxicity sparing associated to FLASH-RT can be dependent on the architecture of the irradiated organ/tissue, being more important for serial organs, which are more sensitive to large local doses than to average doses.

• The paper demonstrates that FLASH-RT sparing intensifies in serial organs with lower volume effect (n) values, significantly reducing NTCP compared to conventional radiotherapy.
• It employs both a radiolytic oxygen depletion model and a phenomenological logistic model to capture the local, dose-dependent FLASH effects integrated with LKB analysis.
• The study highlights that spatial dose inhomogeneity and organ-specific architecture critically influence treatment planning to optimize normal tissue protection during FLASH-RT.

Modeling the Impact of Dose Distribution and Organ Architecture on Toxicity in FLASH Radiotherapy

Introduction

This work provides a comprehensive in silico investigation of how the spatial distribution of radiation dose and the architectural classification of organs (serial versus parallel) modulate normal tissue sparing in FLASH radiotherapy (FLASH-RT) relative to conventional radiotherapy (CONV-RT). The paper directly addresses a critical gap: while experimental studies show pronounced normal tissue sparing with homogeneous FLASH irradiation, the distribution of clinical doses is inherently heterogeneous, and organ responses to such distributions are strongly architecture-dependent. The hypothesis is that the biological advantage of FLASH-RT may depend not solely on physical parameters such as dose and dose rate, but also on the organ’s architectural response mechanism, especially if the underlying FLASH effect is driven by local, rather than systemic, mechanisms.

Methodological Framework

The investigation utilized two principal strategies for modeling the FLASH effect:

1. Radiolytic Oxygen Depletion (ROD) Model: The oxygen depletion hypothesis was implemented via coupled partial and ordinary differential equations governing spatio-temporal dynamics of tissue oxygenation and its impact on clonogenic survival. These equations were numerically solved to derive oxygen-dependent radiobiological parameters, integrating the LQ formalism and explicit oxygen enhancement ratio (OER) dependence.
2. Phenomenological Logistic Model: This approach captures the FLASH effect as a local, intensity-dependent phenomenon via a Hill-type logistic function relating modifying factor to dose and dose rate.

Both approaches translated the local effect into a dose-modifying methodology for each voxel, producing an effective dose distribution for FLASH-RT, subsequently passed into an LKB-based NTCP analysis. The Lyman-Kutcher-Burman (LKB) model, parameterized by the volume effect parameter $n$, allowed exploration of the entire spectrum from pure parallel ($n=1$) to near-serial ($n \to 0$) tissue architectures with carefully controlled reference endpoints.

Key Results

Both ROD-based and phenomenological models demonstrated consistent NTCP reductions for FLASH-RT compared with CONV-RT across all organ architectures. Notably:

• FLASH sparing intensifies as $n$ decreases: The magnitude of NTCP reduction due to FLASH was greater for lower $n$, with maximal effect for highly serial organs (e.g., $\text{NTCP}_{\rm{FLASH}}\approx0.11$ for $n=0.1$ versus $0.14$ for $n=1$ at a reference CONV-RT NTCP of $0.2$).
• Oxygen dependence: For the ROD model, FLASH sparing is strongly modulated by oxygenation, with hypoxic (e.g., 6 mmHg) regions benefiting more than well-oxygenated tissue, except that extremely hypoxic subvolumes are insensitive due to negligible further depletion. For spatially heterogeneous oxygen distributions, the interplay is complex, driven largely by the least-oxygenated voxels.
• Dose inhomogeneity and organ sensitivity: For a fixed inhomogeneous dose distribution, organs whose toxicity is driven by maximum local dose (serial, low $n=1$0) manifest greater absolute and relative benefits from FLASH-RT, consistent with theoretical predictions if mechanisms underlying the FLASH effect are local.

These findings were robust across both the mechanistically detailed ROD model and the phenomenological logistic model. The results make the explicit claim that if the FLASH mechanism is fundamentally local in nature, then spatial dose and organ response heterogeneity will systematically amplify normal tissue sparing in serial architectures.

Theoretical Implications

The results formalize the dependence of FLASH benefit on organ architecture, supporting theoretical and clinical planning efforts to optimize the normal tissue protection in situ based on anatomical and functional metrics. Contrasting conventional wisdom where mean dose dominates toxicity estimation, this work predicts that in FLASH regimens, the architectural parameter $n=1$1 acquires additional importance. For organs characterized by serial failure modes (e.g., spinal cord), localized exposure to high FLASH doses will be more efficiently compensated than for parallel-mode organs (e.g., liver).

Such architectural dependence will have material consequences for patient selection, organ-at-risk prioritization, and fractionation/bioeffect modeling in translational FLASH protocols. The fundamental requirement that the underlying mechanism of FLASH-RT acts locally is a critical assumption. Should systemic mechanisms (e.g., lymphocyte sparing or immune modulation) dominate, these architectural dependencies would be attenuated or absent.

Practical Perspectives and Limitations

The practical implications include the necessity to account for local dose-rate distributions in clinical planning—simply ensuring that the mean dose rate meets FLASH thresholds may not be sufficient for optimal benefit. Additionally, the investigation relies on specific assumptions:

• Dose-rate allocation within the organ is proportional to the local dose, with continuous irradiation assumed, which best models wide-field electron or transmission proton FLASH.
• Only single-fraction delivery was studied, maximizing the observable FLASH effect.
• The FLASH modifying factor and underlying biological parameters were selected according to prevailing experimental evidence but may need context-dependent refinement.

Further, the modeling does not consider temporal microstructure of pulsed beams, interplay effects between fractionation, and potential contribution of systemic effects. The study highlights these as essential future directions to solidify predictions for clinical translation.

Future Outlook

This modeling work motivates further preclinical and clinical studies with serial and parallel organs to empirically validate the predicted architecture dependence of FLASH sparing. There is a clear path for extending the model to complex dose-rate structures, multifraction regimens, and combined local/global mechanisms, as well as for using it as a tool for treatment planning system (TPS) development for FLASH-RT. Additionally, refining parameter selection with in vivo radiobiological data and high-resolution dosimetry remains critical for facilitating robust application.

Conclusion

This study provides a quantitative foundation for the hypothesis that the degree of normal tissue sparing achievable with FLASH-RT in heterogeneous irradiation is modulated by organ architecture, with greater benefit for serial than for parallel organs under the assumption of a local FLASH mechanism. Both mechanistic and phenomenological modeling approaches confirm that maximal local dose exposure is the critical determinant of FLASH-RT sparing in the presence of architectural dose-response heterogeneity. These results provide actionable guidance for the design and interpretation of future experimental and clinical FLASH studies and underscore the importance of integrating architectural sensitivity into radiotherapy plan evaluation and optimization.