Defining high-viscosity, large-volume drug delivery systems
Published: October 2024
Kyle Toole
Design Consultant
Blair Hutton
Design Consultant
James McLusky
Director
Also featured in ONdrugDelivery.
Recent advancements in biologics have introduced breakthrough therapies for a variety of indications. However, these formulations often require higher viscosities and larger volumes for administration, presenting significant challenges in the development of new drug delivery devices for subcutaneous injection. At the same time, these devices must meet the broader needs of both patients and healthcare providers.
Meeting these needs requires the consideration of core factors such as patient tolerability, the formation and dispersion of the subcutaneous depot, device usability, choice of primary container and the technical capabilities of the delivery device itself. One crucial performance requirement that influences the ability of any device to address these factors is the injection duration and the forces required to achieve it.
As shown in Figure 1, there are multiple delivery systems available, or emerging, into the drug delivery landscape. Using mathematical modelling and explorative laboratory testing early in the development process, the engineering team can quickly understand the capabilities and limitations of an established device or the need for a new concept in direct relation to a new drug formulation. This insight enables the efficient evaluation of a concept, helping to define the delivery strategy and the design of next-generation drug delivery systems with informed decisions.
Mathematical modelling and explorative laboratory testing allow us to:
- Define the most suitable device format, along with the associated primary container and needle combination.
- Optimise the often-conflicting design variables of the concept.
- Determine if the concept can still perform at its operating limits.
Mathematical modelling
Hagen-Poiseuille Equation
Using a modified Hagen-Poiseuille equation (Figure 2), we can calculate the nominal injection duration for a given configuration. This equation effectively models injection duration for high-viscosity Newtonian formulations, with reasonably accurate results. Before moving on it should be noted that non-Newtonian fluids, such as formulations that exhibit shear thinning behaviour, require alternative models.
The parameters of the modified Hagen-Poiseuille equation are listed below, and we will discuss them in more detail.
- Viscosity and volume, including environmental factors
- Needle selection
- Primary container
- Plunger stopper friction
- Tissue back pressure
- Drive system force
1. Viscosity and volume: Known or theoretical viscosity and volume data are added into the model to assess how they impact injection duration across different delivery device concepts.
Environmental factors should also be considered. Whilst room temperature is often controlled in clinical settings, patients administering at home encounter temperature ranges that can significantly affect viscosity, even after accounting for ‘warm-up’ time post-refrigeration. Many biologics are sensitive to temperature changes, so using “temperature Vs. viscosity” data in the model helps predict how injection duration might vary in actual use. Refining the device design and informing any mitigating steps that may be added to the Instructions for Use (IFU).
2. Needle selection: Choosing the right needle has long been understood as key for both patient comfort and effective drug delivery. The needle’s gauge, wall thickness, and length significantly influence fluid flow. Smaller diameter needles, reduce patient discomfort but can restrict fluid flow and may increase the risk of occlusion. Conversely, larger diameter needles improve fluid flow but increase patient discomfort.
The use of the Hagen-Poiseuille equation clearly shows that the flow rate is inversely proportional to the fourth power of the needle’s inner radius, emphasising how needle diameter affects injection duration. Balancing these factors increasingly points towards the use of thin-walled or ultra-thin-walled needles. What may look like a small increase in bore diameter can have a huge impact on injection duration, refer to Figure 3.
3. Primary container: The inner diameter of the primary container is crucial because it influences the force required to expel the formulation. Larger diameters may require more force to achieve a target injection duration as the applied pressure equals force divided by area, thus increasing the burden on the delivery device. Additionally, the primary container’s aspect ratio—whether it has a large diameter with a short length or a small diameter with a long length—affects the device’s overall format and usability. Whilst numerous other factors influence the selection of a primary container, an early evaluation of how it integrates into a device and the associated impacts on performance and usability can assist in making efficient decisions.
4. Plunger stopper friction: The glide force of the plunger stopper moving through the primary container, is influenced by the stopper material and design, barrel material, surface treatment, and level of lubrication. Known or expected values can be incorporated into calculations to account for the additional forces the device must overcome to achieve the target injection duration.
5. Tissue back pressure: A factor often overlooked during the characterisation of a concept is tissue back pressure. Typically, combination products are tested by ‘injecting’ into free air. However, injecting into the patient’s subcutaneous tissue introduces back pressure, which can increase both the nominal injection duration and its variability, especially with high-viscosity, large-volume formulations.
Factors influencing tissue back pressure include tissue characteristics at the injection site, formulation composition, viscosity, volume, and flow rate. Analysing data from literature and specific studies allows the incorporation of tissue back pressure values into the equation, improving our understanding of its impact on injection duration.
6. Drive system force: The Hagen-Poiseuille equation can also be rearranged to focus on the required force to achieve a given injection duration. This allows a design team to quickly evaluate concepts for the device form factor and determine suitable drive system technology options. Ensuring the selected concept will meet performance requirements and remains aligned to the overall program strategy.
Monte Carlo simulation
Integrating the Hagen-Poiseuille equation within a probabilistic mathematical model expands our understanding of a concept’s capabilities and limitations by accounting for potential variations and production tolerances. A Monte Carlo simulation is a powerful tool to help in this evaluation.
Whereas the Hagen-Poiseuille equation offers predictions under nominal conditions or simple edge cases, Monte Carlo simulations extend this by modelling a broad range of scenarios. This method generates a predictive distribution or ‘bell curve’ that reveals potential variations in injection duration and identifies the performance limits. Analysis through this approach illustrates how different device configurations may perform under diverse conditions, identifying potential issues. This simulation step ensures a robust concept throughout the development process with a view toward high-volume manufacture.
Explorative laboratory testing
Whilst mathematical modelling is invaluable for exploring concepts and understanding any limitations, empirical data from laboratory testing provides the most reliable insights. Early in the development process, the fluid path can be simulated using off-the-shelf components to compare against the theoretical data.
Equipment such as a Universal Test Machine or syringe pump can simulate a drive system under nominal, best-case, and worst-case conditions, whereas in-line pressure monitoring systems record pressure data. This setup, used in a suite of tests or Design of Experiments studies, offers valuable insights into the forces and pressures required to achieve target injection durations.
If the drug product formulation is not yet available or if a range of viscosities needs exploration, viscosity mimics can be prepared. These mimics, verified with a viscometer, can be filled into the primary container or fluid path for testing. This approach not only develops confidence in the mathematical models but also helps identify discrepancies or unexpected challenges early. Following this initial exploratory testing, physical prototypes of the delivery device can be designed and integrated into development rigs, paving the way for the subsequent design and development stages.
Tackling the challenge of high-viscosity, large-volume drug delivery devices
Developing delivery devices for the subcutaneous administration of high-viscosity, large-volume biologics benefits from an integrated approach that combines mathematical modelling with empirical testing. Using tools such as the Hagen-Poiseuille equation and Monte Carlo simulations early in the development process helps to guide the selection of the optimal device format, balance design variables, and assess performance limits.
Complementing these theoretical models with explorative laboratory testing builds confidence in the predictions and evaluates real-world performance. This combined approach significantly strengthens the likelihood that a drug delivery concept will meet the stringent performance requirements as it progresses through the development process toward high-volume production.
Finally, this approach is not just to inform new delivery system developments, which can be prohibitively expensive. The early engagement with device designers in any pharmaceutical formulation process can quickly review options that may, or may not be suitable for existing platform devices, and categories as illustrated in figure 1. Potentially exposing the need to explore lower concentration at larger volumes or higher concentrations at smaller volumes in a timely manner.
Whatever the overall strategy, this considered approach will optimise therapeutic efficacy, improve patient experience and significantly reduce commercialisation costs.
If you’d like to discuss anything mentioned in this article, please contact our Business Development Manager, Holly Milston.
