A Rigorous Theoretical Framework for Non-Surgical Precision Management of Prostate Cancer: Hierarchical Fusion of Graph Attention Networks, Vision Transformers, and Reinforcement Learning for Spatiomolecular Reasoning and Adaptive Therapeutic Regimens
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2026
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| _version_ | 1866901888784400384 |
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| author | Shibah, Sami Rashid Mohammed |
| author_facet | Shibah, Sami Rashid Mohammed |
| contents | <p>Prostate cancer (PCa) exhibits profound spatiotemporal genomic and radiomic heterogeneity that invalidates static, unimodal clinical decision paradigms. This manuscript presents a theoretically self-contained, mathematically rigorous conceptual framework---the Prostate Precision Fusion Platform (PPFP)---for non-surgical personalized management of localized disease and adaptive combination therapy design in metastatic castration-resistant prostate cancer (mCRPC). </p> <p>PPFP is founded upon a hierarchical information-theoretic integration of three advanced AI modalities: (i) a 3D Vision Transformer (ViT-B/16) with convolutional tokenization for volumetric radiomic feature extraction from mpMRI and PSMA-PET/CT, (ii) a Graph Attention Network v2 (GATv2) operating over spatially-informed protein-protein interaction graphs to derive a 512-dimensional latent molecular embedding with dynamic, context-sensitive attention coefficients (resolving static attention limitations), and (iii) a 12-layer cross-attention transformer fusion engine whose forward pass is proven to maximize a lower bound on multimodal mutual information. </p> <p>For localized PCa (Stratum A), the fusion embedding drives a Personalized Non-Invasive Risk Index (PNIRI) regression head, for which we establish finite-sample generalization bounds and demonstrate through global Sobol sensitivity analysis and a granular Monte Carlo parameter grid that the model is highly robust to input perturbations up to 15% additive Gaussian noise (AUC variance < 0.02). For mCRPC (Stratum B), we formulate therapy selection as a partially observable Markov decision process (POMDP) solved via Proximal Policy Optimization (PPO). Crucially, we provide a closed-form definition of the transition dynamics P via a coupled system of Ordinary Differential Equations (ODEs) modeling tumor burden evolution, pharmacokinetics, and the emergence of subclonal resistance, thereby completing the full mathematical specification of the POMDP.</p> <p>The framework's generality is demonstrated by a formal morphism to breast cancer applications, where identical GATv2 dynamic attention mechanisms predict trastuzumab response in HER2-enriched and PARPi sensitivity in triple-negative subtypes. All derivations, including the complete Python Monte Carlo simulation code with fixed seed reproducibility, parameter justifications, Sobol indices, sensitivity grids, and high-fidelity TikZ/PGFPlots visualizations, are embedded within this manuscript to ensure complete self-sufficiency, falsifiability, and rigorous internal consistency.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19693899 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Rigorous Theoretical Framework for Non-Surgical Precision Management of Prostate Cancer: Hierarchical Fusion of Graph Attention Networks, Vision Transformers, and Reinforcement Learning for Spatiomolecular Reasoning and Adaptive Therapeutic Regimens Shibah, Sami Rashid Mohammed <p>Prostate cancer (PCa) exhibits profound spatiotemporal genomic and radiomic heterogeneity that invalidates static, unimodal clinical decision paradigms. This manuscript presents a theoretically self-contained, mathematically rigorous conceptual framework---the Prostate Precision Fusion Platform (PPFP)---for non-surgical personalized management of localized disease and adaptive combination therapy design in metastatic castration-resistant prostate cancer (mCRPC). </p> <p>PPFP is founded upon a hierarchical information-theoretic integration of three advanced AI modalities: (i) a 3D Vision Transformer (ViT-B/16) with convolutional tokenization for volumetric radiomic feature extraction from mpMRI and PSMA-PET/CT, (ii) a Graph Attention Network v2 (GATv2) operating over spatially-informed protein-protein interaction graphs to derive a 512-dimensional latent molecular embedding with dynamic, context-sensitive attention coefficients (resolving static attention limitations), and (iii) a 12-layer cross-attention transformer fusion engine whose forward pass is proven to maximize a lower bound on multimodal mutual information. </p> <p>For localized PCa (Stratum A), the fusion embedding drives a Personalized Non-Invasive Risk Index (PNIRI) regression head, for which we establish finite-sample generalization bounds and demonstrate through global Sobol sensitivity analysis and a granular Monte Carlo parameter grid that the model is highly robust to input perturbations up to 15% additive Gaussian noise (AUC variance < 0.02). For mCRPC (Stratum B), we formulate therapy selection as a partially observable Markov decision process (POMDP) solved via Proximal Policy Optimization (PPO). Crucially, we provide a closed-form definition of the transition dynamics P via a coupled system of Ordinary Differential Equations (ODEs) modeling tumor burden evolution, pharmacokinetics, and the emergence of subclonal resistance, thereby completing the full mathematical specification of the POMDP.</p> <p>The framework's generality is demonstrated by a formal morphism to breast cancer applications, where identical GATv2 dynamic attention mechanisms predict trastuzumab response in HER2-enriched and PARPi sensitivity in triple-negative subtypes. All derivations, including the complete Python Monte Carlo simulation code with fixed seed reproducibility, parameter justifications, Sobol indices, sensitivity grids, and high-fidelity TikZ/PGFPlots visualizations, are embedded within this manuscript to ensure complete self-sufficiency, falsifiability, and rigorous internal consistency.</p> |
| title | A Rigorous Theoretical Framework for Non-Surgical Precision Management of Prostate Cancer: Hierarchical Fusion of Graph Attention Networks, Vision Transformers, and Reinforcement Learning for Spatiomolecular Reasoning and Adaptive Therapeutic Regimens |
| url | https://doi.org/10.5281/zenodo.19693899 |