Predictive Dosimetry in PSMA-Targeted Radiopharmaceutical Therapies: A PBPK Modeling and Machine Learning Study

Predictive dosimetry is central to enabling personalized radiopharmaceutical therapy (RPT), particularly in prostate specific membrane antigen (PSMA) targeted theranostics. In this work, we develop a three layer computational framework that integrates physiologically based pharmacokinetic (PBPK) modeling with machine learning (ML) to predict both physical (AUC, absorbed dose) and biological (BED, EQD2) dosimetric endpoints in tumors and major organs. In the first layer, we generated 640 virtual patients using PBPK simulations of F-18, Ga-68, and Cu-64 labeled PSMA PET tracers paired with Lu-177 PSMA therapy, producing 15360 tumor and organ time activity curves (TACs) under realistic biological variability and PET-like noise. In the second layer, TACs were transformed into quantitative kinetic features and mapped to physical and biological dose metrics. In the third layer, ML models (Random Forest, Extra Trees, Ridge, Gradient Boosting, and XGBoost) were trained to predict RPT doses from PET derived features, with performance evaluated using mean absolute percentage error (MAPE) and R2. Cu-64 PSMA-617 based PET yielded the most robust predictions, achieving tumor dose MAPE as low as 8 percent and 10 to 20 percent for normal organs, while F-18 DCFPyL showed volume dependent performance and Ga-68 PSMA-11 exhibited higher variability. SHAP analysis revealed that peak uptake, clearance, and early kinetic features dominated predictive performance across organs and endpoints. This PBPK ML framework enables scalable, physiology informed predictive dosimetry and provides a foundation for trial design and patient specific treatment planning in PSMA targeted RPT. These results demonstrate that pre therapy PET can serve as a reliable surrogate for post therapy dosimetry, enabling scalable personalization of PSMA targeted RPT.

💡 Research Summary

This paper presents a three‑layer computational framework that combines physiologically based pharmacokinetic (PBPK) modeling with machine‑learning (ML) to predict both physical (AUC, absorbed dose) and biological (BED, EQD2) dosimetric endpoints for PSMA‑targeted radiopharmaceutical therapy (RPT). In the first layer, the authors extended a previously validated PSMA‑PBPK model to simulate the kinetics of three PET tracers (^18F‑DCFPyL, ^68Ga‑PSMA‑11, ^64Cu‑PSMA‑617) and the therapeutic agent ^177Lu‑PSMA‑I&T. They generated 640 virtual patients by sampling key physiological and molecular parameters (organ volumes, blood flow, receptor density, association/dissociation rates, internalization and release rates, renal extraction) within literature‑derived bounds and scaling them to individual height and body‑surface area. For each virtual patient, time‑activity curves (TACs) were produced for tumor and major organs over a 30 000‑minute window (≈500 h), yielding 15 360 TACs. PET‑like noise was added to the PET‑tracer TACs using a log‑normal model proportional to the square root of the mean activity, while therapy TACs remained noise‑free to serve as ground truth.

The second layer extracts a comprehensive set of 30 kinetic descriptors from each PET‑TAC, including peak activity (AMax), time to peak (Tmax), minimum activity, mean, standard deviation, median, skewness, kurtosis, Shannon entropy, total energy, area under the curve (AUC), half‑life, clearance ratios, percentile values, and slope‑based metrics (max/min slopes, rise/fall times). These features constitute the ML input space. From the therapy TACs, cumulative exposure, dose‑rate, absorbed dose, biologically effective dose (BED), and equivalent dose in 2 Gy fractions (EQD2) were computed using standard radionuclide decay and radiobiological formulas.

In the third layer, five regression algorithms—Random Forest, Extra Trees, Ridge, Gradient Boosting, and XGBoost—were trained to map PET‑derived kinetic features to each dosimetric endpoint for each organ (tumor and normal tissues). A strict five‑fold patient‑level cross‑validation ensured that all TACs belonging to a given virtual patient were kept within the same fold, preventing information leakage. Model performance was evaluated with mean absolute percentage error (MAPE) and coefficient of determination (R²). The ^64Cu‑PSMA‑617 PET‑based models achieved the best results, with tumor dose MAPE as low as 8 % and R² ≈ 0.92; normal organ dose predictions were within 10‑20 % MAPE. ^18F‑DCFPyL showed volume‑dependent performance, and ^68Ga‑PSMA‑11 exhibited the highest variability. SHAP (Shapley Additive Explanations) analysis identified peak uptake (AMax), time to peak (Tmax), early clearance, and early slope features as the dominant contributors across all organs and endpoints, underscoring the importance of early kinetic information for accurate dose prediction.

The authors argue that this PBPK‑ML pipeline constitutes a “digital twin” platform suitable for virtual clinical trials, enabling rapid exploration of dosing strategies, patient stratification, and protocol optimization before actual patient enrollment. By simulating a broad spectrum of physiological variability, the framework can generate synthetic datasets that train robust ML models, which in turn can infer post‑therapy dosimetry from a single pre‑therapy PET scan. This approach promises to replace empirical weight‑based activity prescriptions with personalized dose‑guided regimens, potentially improving therapeutic efficacy while reducing toxicity.

Limitations include reliance on simulated data; external validation with real patient PET and post‑therapy dosimetry is required. The PET noise model, while realistic at the ROI level, does not capture reconstruction artifacts or motion‑induced errors present in clinical images. Additionally, radiobiological parameters (e.g., α/β ratios) were fixed, which may limit applicability across diverse tumor histologies. Nonetheless, the study demonstrates that integrating mechanistic PBPK simulations with modern ML yields a scalable, physiology‑informed predictive dosimetry tool that could accelerate personalized PSMA‑targeted RPT and inform future theranostic trial designs.