(25b) Development of Hybrid Models for Predicting Delivery Time in Autoinjector Systems

Autoinjectors (AJs) are critical medical devices designed to deliver precise doses of medication via intramuscular or subcutaneous injections. They offer several advantages over conventional delivery methods, including ease of use and improved dosage accuracy, which has led to their growing importance in recent years (Roy et al., 2020). These devices consist of multiple components that ensure safe and reliable drug administration, making the design of these components essential for device reliability and safety. Among the key parameters in AJ devices, injection time is particularly crucial. If the injection time is too prolonged, patient comfort significantly decreases, and there is a risk that the patient may terminate the injection before administering the full dose. Conversely, if the injection is too rapid, it could compromise the device’s integrity and increase injection pain. Thus, injection time is a critical factor in ensuring accurate dosing, maintaining device durability, preserving drug stability, and ensuring patient comfort. A comprehensive assessment of injection time is therefore essential during the design phase of AJs.

To predict injection time, it is crucial to first understand the injection process and the forces at play. This process is influenced by two primary forces: hydrodynamic and frictional forces. The hydrodynamic force, governed by the system’s rheology, is dependent on the geometrical properties of the autoinjector (AJ) and the fluid characteristics. Models for hydrodynamic forces have proven to be reliable. In contrast, modelling friction is more complex due to the underlying physical phenomena, with various models of differing complexity proposed to quantify friction (Rathore et al., 2011; Zhong et al., 2022). All mechanistic models agree that friction in AJs is determined by the plunger speed and the nature of the contacting surfaces. However, experimental data on injection times reveal a correlation between the extrusion force required for injection and the syringe piston’s travel distance. Therefore, existing models in the literature are inadequate for accurately predicting injection time in AJs.

Furthermore, the system under analysis exhibits significant variability due to several parameters affecting frictional force, such as the trim edge, which are unknown and cannot be measured in advance. As a result, a robust model must effectively address this uncertainty.

This study presents a novel hybrid model to predict delivery time in AJs, integrating physics-based elements from established literature models with data-driven components that employ state estimation techniques such as Kalman Filters (Galvanin et al., 2012), Gaussian processes (Petsagkourakis et al., 2021, Friso et al. 2024), or artificial neural networks (ANN). By incorporating additional variables overlooked by traditional models, our hybrid approach seeks to enhance both accuracy and predictive capability. The development of this hybrid model presents various challenges. To ensure its robustness and reliability, we address the issue of structural identifiability (Walter et al., 1997) by thoroughly examining the model structure and the estimability of its parameters. This is accomplished through a comprehensive sensitivity analysis to identify key parameters that significantly impact injection time. The findings from the identifiability study will guide the development of alternative hybrid models and support model-based experimental design efforts for the precise characterization of delivery time in AJs.