One scale to rule them all: interpretable multi-scale Deep Learning for predicting cell survival after proton and carbon ion irradiation

Technical Summary: One Scale to Rule Them All: Interpretable Multi-scale Deep Learning for Predicting Cell Survival

Problem Statement
The relationship between the physical characteristics of radiation fields and biological damage is central to radiotherapy and radioprotection. However, the link between the spatial scales of energy deposition (nanometer, micrometer, and macroscopic) and biological effects remains not entirely understood. Traditional radiobiological modeling often relies on a single spatial domain—such as Linear Energy Transfer (LET) for macroscopic averages, microdosimetry for cellular scales, or nanodosimetry for DNA-sized volumes—neglecting the underlying complexity of radiation stochasticity across different scales. A critical open question is whether a specific domain size exists that is most relevant for predicting biological effects, or if these scales are complementary. Furthermore, while Deep Learning (DL) offers high predictive accuracy, its "black box" nature limits its utility in clinical settings where interpretability and mechanistic insight are required.

Methodology
To address these challenges, the authors developed an interpretable Deep Learning model trained on the Particle Irradiation Data Ensemble (PIDE) dataset, which contains cell survival experiments for protons and carbon ions.

• Data Augmentation: The study augmented the PIDE dataset by simulating additional physical descriptors beyond conventional macroscopic parameters. Using the MC-STARtrack and Open-TOPAS Monte Carlo toolkits, the authors generated:
  • Nanodosimetric quantities: Specifically, the complementary cumulative distribution function $F^*(n)$ of ionization cluster sizes within DNA-sized volumes, which correlates with complex DNA damage.
  • Microdosimetric quantities: Frequency-mean ($\bar{y}_F$) and dose-mean ($\bar{y}_D$) lineal energy, simulated in 1-$\mu$m water spheres representing cell nuclei.
  • Macroscopic quantities: Standard LET and dose values.
• Model Architecture: The core of the approach is a TabNet-based architecture employing a sequential attention mechanism. Unlike standard neural networks, this model operates through a sequence of decision steps. At each step, an attentive transformer produces a sparse feature selection mask (using the Sparsemax function) to dynamically select relevant input features.
  • Interpretability: The model utilizes a feature prior that discourages the repeated selection of the same features across steps, promoting diverse feature selection. A sparsity regularization term based on the entropy of attention masks is added to the training objective. This design ensures "native interpretability," allowing the model to highlight which spatial scales contribute to the decision at each step without requiring post-hoc explanation tools like SHAP.
• Training and Evaluation: The model was trained to predict cell survival parameters derived from the Linear-Quadratic (LQ) formalism. Performance was evaluated using Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) on independent folds of the dataset. The model's predictions were compared against established clinical models: the Microdosimetric Kinetic Model (MKM) and the Local Effect Model (LEM) version III.
• Endpoints: The study focused on three biologically significant endpoints:
  1. The dose to 10% survival ($D_{10}$), used for calculating Relative Biological Effectiveness (RBE).
  2. Survival at 2 Gy (conventional fractional dose).
  3. The initial slope of the survival curve (low-dose limit), reflecting intrinsic radiosensitivity.

Key Results

• Predictive Accuracy: The multi-scale DL model achieved a MAPE of 9.5% for RBE predictions and demonstrated superior performance compared to MKM and LEM. Specifically, the model achieved a mean RMSE of approximately 0.1 for V79 and HSG cell lines, significantly outperforming MKM (0.8 and 0.2, respectively) and LEM (1.3 and 0.5, respectively).
• Feature Importance and Scale Contribution:
  • No Single Dominant Scale: The analysis revealed that no single spatial scale is predominant across all conditions. Instead, the model dynamically combines complementary information.
  • Scale Hierarchy: Quantities defined at smaller spatial domains (nanodosimetry) generally exert a greater influence than macroscopic descriptors. Specifically, the nanodosimetric descriptor $F^*(1)$ consistently exhibited the highest attention across all endpoints.
  • Endpoint Dependence:
    • For $D_{10}$ and 2 Gy, attention was more evenly distributed, with $\bar{y}_D$ and LET emerging as influential after $F^*(1)$.
    • For the low-dose limit, nanodosimetric metrics showed a clear predominance, with only $\bar{y}_F$ approaching comparable importance.
  • Particle and Energy Dependence:
    • Carbon Ions: Nanodosimetry was approximately three times more important for carbon ions than for protons. The model captured the "overkill effect" (decreased biological effectiveness at very high LET) without explicit mathematical saturation terms, relying instead on the interplay of microdosimetric and nanodosimetric features.
    • Protons: Microdosimetry became significantly more important at higher energies, driven primarily by $\bar{y}_F$.
• Radiosensitivity: The model's attention patterns varied based on cell line radiosensitivity (defined by the $\alpha_X/\beta_X$ ratio). Highly radiosensitive lines ($\alpha_X/\beta_X > 4$ Gy) showed more stable attention across scales, whereas less sensitive lines showed increasing attention to microdosimetry and LET with energy.

Significance and Claims
The paper claims that its primary contribution is not merely the introduction of a more accurate predictive model, but the investigation of interpretability in multi-scale radiobiological modeling. By leveraging a transparent DL architecture, the study demonstrates that:

1. Multi-scale Integration is Essential: Accurate prediction of radiation-induced biological effects requires integrating information across nanodosimetric, microdosimetric, and macroscopic scales rather than relying on a single physical descriptor.
2. Data-Driven Mechanistic Insight: The model allows the relative contributions of different spatial scales to emerge organically from the data, free from the structural biases of predefined mathematical models (like LEM or MKM).
3. Clinical Relevance: The framework provides a novel lens to understand how different scales of energy deposition impact biological outcomes, offering insights that could guide the optimization of particle therapy treatment plans.
4. Transparency: The built-in attention mechanism provides native interpretability, addressing a major barrier to the clinical adoption of AI in radiotherapy by offering transparent insights into the model's decision-making process.

The authors conclude that while the current study is limited by the availability of data and the specific endpoints used, the approach offers a transformative opportunity to incorporate detailed physical and biological descriptions into treatment-plan optimization, advancing the precision and personalization of particle therapy.