I assume some of you have been trying to develop a simulation tool to estimate the dosing time for an autoinjector. However, you may have encountered difficulties due to some complicate math and the need for specialized software like MATLAB or Mathcad. I used Mathcad when I worked at a company, but not everyone can afford to purchase these powerful programs. Today, I will share how we can develop a dosing simulation tool using Excel or Python. I have already developed such a tool and have been using it for a long time. Therefore, the simulation tool with Excel has been proven to work accurately.
I recall initially thinking, “Do we need this device for just one shot?” when I first heard about the autoinjector. Nowadays, syringes in autoinjectors are being developed for most new drugs. Additionally, I remember discussing issues like broken components, high viscosity solutions, injection time, spring force, dose accuracy, syringe lubrication, wrinkles on the plunger, break-loose and gliding force, Container Closure Integrity Testing (CCIT) with just the syringe or the entire autoinjector, stress analysis of interference fits with Finite Element Analysis (FEA), retraction points, tolerance stack-up, and more. Wow, there are numerous technologies and fundamental principles involved in autoinjector development.
In my previous work, I used Newton’s second law, F=ma, and ordinary differential equations to run the model in Mathcad. Instead, you can use the force balance equation: Spring Force = Frictional Force + Hydraulic Force. When the spring is activated, the spring force changes at different positions, which we will call Spring force (A). You can also determine Spring force (B) from the force balance equation. The frictional force and hydraulic force vary with speed, which is also dynamically changing. Using the “Solver” function in Excel, you can determine the minimum value of (Spring force (A) – Spring force (B)) by adjusting the speed.
Understanding the force balance and the Solver function enables you to calculate dosing as a function of time and track changes in force over time. Figures 1 and 2 illustrate graphs generated from Excel, while Figures 3 and 4 display results from Python. As a device development engineer, it is crucial to invest time in comprehending the force balance and developing this dosing model. Doing so will enhance your ability to innovate and optimize autoinjector designs.
