Quaternion-based recurrent neural networks and machine learning for 3D modeling of superficial femoral artery dynamics: a theoretical framework for enhanced treatment outcomes

The superficial femoral artery (SFA) is highly susceptible to atherosclerotic disease, with restenosis rates which are exceeding 30%–50% following endovascular intervention. Current diagnostic approaches including two-dimensional angiography and duplex ultrasound are failing to capture the complex three-dimensional (3D) spatiotemporal dynamics of vessel remodeling during physiological motion. This theoretical framework is integrating quaternion-based recurrent neural networks (QRNNs) with machine learning pipelines to model dynamic 3D changes in SFA geometry from serial imaging data or continuous recording of SFA quaternion dynamics during activities by wearable Internet of Things devices. Quaternions are providing a singularity-free representation of 3D rotations, while QRNNs are processing quaternion-valued sequences through Hamilton product operations. The integrated pipeline is combining 3D convolutional neural network encoders for feature extraction, QRNN cores for temporal sequence modeling, and conditional generative adversarial networks for synthetic geometry generation. A multi-objective loss function is balancing quaternion prediction accuracy, geometric feature errors, geometric realism, and probability calibration. The framework is theoretically enabling predictive 3D modeling of vessel remodeling, simulation-driven personalized intervention planning, and quantitative risk stratification for restenosis. By grounding the approach in rigorous quaternion mathematics, QRNNs could achieve improved fidelity in capturing dynamic vessel behavior compared to Euclidean approximations. This theoretical framework may be able to address critical gaps in current treatment approaches and is demonstrating a potential for transforming SFA 3D analysis and peripheral artery disease management, once it has been tested and validated.