Mathematical modelling of injection time in autoinjectors: State of the art and future perspectives

Autoinjector devices are a specialized type of medical equipment used for the self-administration of medications. Over the past decade, the significance in these devices has increased, both in terms of their usage and academic interest. An important parameter to be characterized in these devices is the injection time, defined as the duration required to deliver the correct amount of medication. Due to the growing interest in autoinjectors, there has been a pressing need to develop mathematical models for their design and optimization. This review paper presents an analysis of the different mathematical models used to understand and describe autoinjectors devices. Models are analysed, with key characteristics highlighted to showcase the advantages and disadvantages of each in different applications. In comparing these models, the trade-off between accuracy and precision of the predictions are discussed, as well as the importance of validating the models under different conditions. The implications for future research in this field are discussed, emphasizing the need for improved parameter estimation and standardized validation protocols. By addressing current limitations and leveraging advancements in technology, such as multi-physics modelling and machine learning, the field can advance towards more effective and reliable autoinjector designs, ultimately improving patient outcomes and expanding the utility of these devices.