# Product Resistance (Rp): Methods of Measurement and Factors Affecting it

The resistance to vapor flow through the dried layer out of the vial during primary drying is known as product resistance (Rp). Product resistance is a vital decider of the product temperature, together with the vial heat transfer coefficient (Kv).

It can supply structural information about cake morphology instantly at the point of measurement but quantifying Rp is the weakest part of any predictive model of primary drying.

Dr. Robin Bogner from the University of Connecticut, USA, recently held a webinar that outlined the components affecting product resistance and methods to quantify it during primary drying of the lyophilization cycle for products in vials. This article summarizes the webinar.

## Dry product resistance (Rp)

As it affects the product temperature profile, which must be in an optimal range to avoid collapse, maintain the stability of products, and the time to complete primary drying, the Rp is crucial. The Rp will increase with time and thickness of the product layer (Ldry) equally if the dry product is homogeneous.

The relationship between Rp and Ldry can sometimes be non-linear because of shrinkage around sides of vial, product heterogeneity, or product micro collapse. Usually, this association is shown as an empirical equation, Rp = R0 + (A1*Ldry/(1 + A2*Ldry)) with a constant (Ro) and refers to resistance at Ldry = 0 and two coefficients (A1 and A2).

## Factors which affect Rp

It is worth considering the factors that affect this resistance, as Rp is so vital to lyophilization and how these can be altered to optimize the freeze-drying process for a given product.

### Formulation

By nature, formulation materials possess different resistances and so each product formulation could have different dry product resistance during freeze drying. These differences slow the sublimation process as they act as a physical barrier for vapor flow through the dried layer.

It is possible to misinterpret recent work to suggest that only formulation and concentration and influence Rp (Shivkumar et al. 2019 and Pikal et al., 2018) but there is also proof that the freezing protocol, as well as product micro collapse created with different shelf temperatures approaching the glass temperature of a formulation (Tg’), may influence the Rp value (Lewis et al., 2010) (Figure 1).

Figure 1. Microcollapse above the Tg’ lowers the dry layer resistance. Image Credit: SP Scientific Products

### Ice nucleation temperature

Studies have demonstrated that high freezing rates and higher ice nucleation temperature (lower degree of supercooling) result in lower resistance, irrespective of whether the nucleation is controlled or not (Searles et al., 2001).

### Rate of freezing

When comparing slow (ice nucleation at -5 °C and cool at 0.2 °C/ min) and fast (ice nucleation at -10 °C and cool at 5 °C/ min) freezing of an amorphous formulation of 100 mg/mL protein, it is clear that the smaller pores generated during the quicker freezing result in higher Rp values.

### Annealing

By holding a product at a predetermined temperature for a specified duration, annealing is frequently utilized in freeze-drying to prompt crystallization. This can lower the primary drying time by growing ice crystal sizes with more pores on the cake. In the webinar, studies were discussed, which show that an increase in primary drying rate reduces the Rp when above Tg’, but not below Tg’ (Searles et al., 2001).

Other factors that may affect Rp values include phase transitions during the freezing and drying cycles, vial dimensions, which influence the freezing rate and pattern, all of which are formulation dependent. The Rp should ideally be quantified by utilizing the same formulation, fill, vial, freezing, and primary drying protocols as expected for the target cycle.

## Techniques to measure Rp

A number of techniques can be used to measure the value of Rp that takes into consideration if the product is in real time or time-averaged, is in a batch or a single vial, and with controlled or uncontrolled nucleation. Each of these scenarios was outlined in the webinar, but how Rp can be measured for a batch of samples will be outlined in this article.

One of the most common techniques used for measuring Rp using the pressure rise within the chamber is Manometric temperature measurement is (MTM). An isolation valve between the two chambers is closed very quickly and the rise in pressure can be measured over about 25 secs.

The Rp value can be calculated with this information using a complex equation that considers a number of other parameters, including Ldry. Some systems may have a SMART MTM, which generates a spreadsheet of all the appropriate data as soon as the measurement is taken to plot the Rp and Ldry.

The batch average real-time sublimation rate can be calculated from a heat flux sensor or Tunable Diode Laser Absorption Spectroscopy (TDLAS) without MTM. For a single vial, if either heat flux data or TDLAS is not available to quantify the sublimation rate, the sublimation rate can be established by utilizing overall drying, average temperature, and heat transfer coefficient.

It is possible to establish the sublimation rate for each vial using the temperature of each thermocouple and the known Kv for each vial. So it is possible to calculate Rp for numerous different systems using the various data available.

## Summary

The freezing protocol has a significant effect on the structure of the dried cake and Rp. There are a number of factors that should be considered when optimizing a lyophilization cycle for a specific formulation, e.g., annealing, micro collapse, formulation, and phase transitions all affect the value of Rp.

According to the available data and technology, measuring Rp is possible using different methods. Batch average Rp and Ldry can be quantified using TDLAS, MTM, and heat flux, but even without this advanced technology, cycle data (product temperature, Kv, and time) can be utilized to supply batch or single vial Rp and Ldry values.

## Acknowledgments

Produced from materials originally authored by Dr. Robin Bogner from the University of Connecticut, USA.

SP is a synergistic collection of well-known, well-established, and highly regarded scientific equipment brands — SP VirTis, SP FTS, SP Hotpack, SP Hull, SP Genevac, SP PennTech, and most recently SP i-Dositecno — joined to create one of the largest and most experienced companies in freeze-drying/lyophilization, complete aseptic fill-finish production lines, centrifugal evaporation and concentration, temperature control/thermal management, glassware washers and controlled environments.

SP is part of SP Industries, Inc., a leading designer, and manufacturer of state-of-the-art laboratory equipment, pharmaceutical manufacturing solutions, laboratory supplies and instruments, and specialty glassware. SP's products support research and production across diverse end-user markets including pharmaceutical, scientific research, industrial, aeronautic, semiconductor, and healthcare. In December 2015, SP Industries was acquired by Harbour Group, a private investment firm founded in 1976. Harbour Group is a privately owned, operations focused company based in St. Louis, Missouri. Headquartered in Warminster, Pennsylvania, SP has production facilities in the USA and in Spain and the UK in Europe and offers a world-wide sales and service network with full product support including training and technical assistance.

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Last updated: Dec 15, 2020 at 10:48 AM

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