Autoinjectors (AJs) are essential medical devices designed to deliver precise dose of medication via intramuscular or subcutaneous injection. Compared to traditional delivery methods, they offer significant advantages, including ease of use and improved dosage accuracy, which have contributed to their growing importance in recent years (Roy et al. 2020). The design of these devices is critical to ensuring both performance and patient safety., as they rely on multiple components to facilitate safe and reliable drug administration. Among the key parameters influencing AJs functionality, injection time plays a particularly crucial role. A prolonged injection time can compromise patient comfort and increase the risk of incomplete dose delivery, while an excessively fast injection may impact device integrity and cause injection pain. Optimizing injection time is therefore essential to ensure the accurate dosing, device longevity, drug stability, and patient adherence, making its thorough evaluation a key aspect of AJ design.
Accurately predicting injection time requires a deep understanding of the forces governing the injection procedure. The primary forces involved are the driving forces, the hydrodynamic forces, and the friction forces. The driving force, which powers the injection, varies depending on the mechanism-such as spring in spring-driven AJs or compresses gases in gas-driven systems. The hydrodynamic forces, dictated by the rheological properties of the drug formulation, depends on both the device’s geometry and fluid characteristics. While hydrodynamic forces models have demonstrated reliability, friction modelling remains a significant challenge due to the complexity of the underlying physical interactions. Several friction models of varying complexity have been proposed, both mechanistic (Rathore et al., 2011; Zhong et al., 2022) and hybrid (Friso et al., 2024). In these friction models friction force in AJs is influenced by the plunger speed and surface interactions between the plunger and the inner wall of the syringe. However, experimental data from force-displacement measurements conducted during injection procedures reveal a correlation between the extrusion force required for injection and the syringe piston’s travel distance, underscoring the limitations of existing models in accurately predicting injection time.
A further challenge in the system is the significant variability, largely due to factors affecting the friction forces-such as the properties of the contacting surfaces between the stopper and the inner syringe wall- that are unknown and cannot be measured a priori. Developing a robust model capable of addressing these uncertainties is therefore essential for reliable injection time prediction. To tackle this issue, Model-Based Design of Experiments (MBDoE) (Franceschini et al., 2008), an advanced methodology for optimizing data collection for model discrimination (MBDoE-MD) or improving parameter estimation (MBDoE-PE), is employed in this work. MBDoE relies on the evaluation of Fisher Information Matrix (FIM), a metric which quantifies the expected amount of information that can be obtained from experiments on model parameters. The FIM is evaluated based on the system’s sensitivity and the variance of experimental measurements. Once computed, it allows for the assessment of parameter uncertainty, as the inverse of the FIM corresponds to the variance-covariance matrix (Zullo 1991). If the estimated parameters lack sufficient accuracy, additional experiments can be planned accordingly. Unlike traditional experimental design, which relies on empirical trial-and-error approaches, MBDoE leverages model knowledge to optimize experimental selection, thereby maximizing the expected information gain. This leads to a more efficient model identification process, reducing the number of required experiments while improving model accuracy and robustness.
Applying MBDoE to AJs offers several key benefits:
- It enables discrimination between different injection time models (mechanistic and hybrid).
- It enhances parameter estimation efficiency, which is particularly important given the inherent variability of the friction forces, allowing experimental conditions to be optimized to reduce parameter uncertainty.
- It minimizes experimental costs, as AJs devices are expensive, and experiments assessing extrusion and friction forces are destructive experiments. Reducing the number of required tests is therefore crucial for cost-effectiveness.
Despite these advantages, integrating MBDoE into AJs modelling presents unique challenges:
- MBDoE is traditionally applied to identify models of unit operations in chemical engineering (Deussen et al. 2022), whereas in this case it is being used to optimize a mechanical device.
- Standard MBDoE applications typically involve a design space where experimental inputs are continuous variables (Cenci et al. 2023), whereas AJ systems are characterised by discrete input variables, as their components have fixed dimensions and vary depending on the supplier.
By incorporating MBDoE into the AJ design process, a more rigorous, efficient, and predictive framework for modelling injection time can be achieved. This not only improves the accuracy of injection time predictions, but it also broadens the scope of MBDoE applications, demonstrating its potential in optimizing complex mechanical systems beyond its conventional chemical engineering application.
References
- Roy A., Geetha R.V., Magesh A., Vijayaraghavan R., Ravichandran V. "Autoinjector - A smart device for emergency cum personal therapy." Saudi Pharm J. 2021 Oct;29(10).
- Rathore N., Pranay P., Eu B., Ji W., Walls E. "Variability in syringe components and its impact on functionality of delivery systems." PDA JPST vol. 65,5 (2011).
- Zhong X., Guo T., Vlachos P., Veilleux J.C., Huaiqiu S. G., Collins D.S., Ardekani A.M. "An experimentally validated dynamic model for spring-driven autoinjectors." International Journal of Pharmaceutics, Volume 594, 2021.
- Friso A., Palmer M., Bano G., Galvanin F., “On the development of hybrid models to describe delivery time in autoinjectors”, Computer Aided Chemical Engineering, Elsevier, Volume 53, 2024.
- Franceschini G., Macchietto S.,” Model-based design of experiments for parameter precision: State of the art”, Chemical Engineering Science, Volume 63, Issue 19, 2008.
- Zullo, L., 1991. Computer aided design of experiments. An engineering approach. Ph.D. Thesis, University of London, UK
- Deussen P., Galvanin F., A model-based experimental design approach to assess the identifiability of kinetic models of hydroxymethylfurfural hydrogenation in batch reaction systems, Chemical Engineering Research and Design, Volume 178, 2022, Pages 609-622.
- Cenci F., Pankajakshan A., Facco P., Galvanin F., An exploratory model-based design of experiments approach to aid parameters identification and reduce model prediction uncertainty, Computers & Chemical Engineering, Volume 177, 2023
