This work introduces a novel integration of Physics-Informed Neural Networks (PINNs) with hyperelastic material modeling, employing the Neo-Hookean model to estimate the stiffness of soft tissue organs based on realistic anatomical geometries. Specifically, we propose the modeling of the prostate biomechanics as an initial application of this framework. By combining machine learning with principles of continuum mechanics, the methodology leverages finite element method (FEM) simulations and magnetic resonance imaging (MRI)-derived prostate models to address forward and inverse biomechanical problems. The PINN framework demonstrates the ability to provide accurate material property estimations, requiring limited data while overcoming challenges in data scarcity. This approach marks a significant advancement in patient-specific precision medicine, enabling improved diagnostics, personalized treatment planning, and broader applications in the biomechanical characterization of other soft tissues and organ systems.

Background/Objectives: Recently, studies have emerged raising ergotrauma as a new explanation for ventilator-induced lung injury development, with the concept of inspiratory Mechanical Power (MP) as a single physical variable to estimate the contribution of different ventilatory parameters to lung damage. A high value of inspiratory MP is associated with risk of harming the respiratory system. Furthermore, we propose the concept of effective MP as the energy per minute that dissipates in the lungs, subtracting expiratory MP from inspiratory MP. Our objective is to validate the equations proposed for adults to estimate inspiratory MP in children, and to develop and validate equations to estimate effective MP. Methods: Prospective convenience sampling of 18 children undergoing mechanical ventilation in volume-controlled ventilation mode, admitted to the pediatric intensive care unit of a tertiary university hospital. Data of ventilation parameters, loops and curves were obtained electronically with the automated procedure provided by the device software and compared with the theoretical results of the equations. Results: Among the available equations for calculating inspiratory MP in adults under volume-controlled ventilation, the simplified Gattinoni and generalized Giosa equations provided the best estimates in children (R² > 0.99). For expiratory MP, the extended equation proposed in this study showed the best agreement with experimental results (R² = 0.9954). Finally, for effective MP, the simplified equation was the most accurate (R² = 0.9950). Conclusions: This study validated existing inspiratory MP equations in pediatric patients and introduced the concept of effective MP, together with a bedside equation for its estimation. Future studies should determine effective MP thresholds associated with ventilator-induced injury.