© Institute for International Research, Inc All rights reserved. Module 5: Optimizing the Process Cycle

2 international Module 5 Purpose and Objectives  Module Purpose:  Process optimization requires understanding the process. The student will get a thorough introduction to Clausius-Clapeyron and Sublimation Kinetics.  Module Objectives:  After this module, you will be able to  Think through a sublimation problem  Predict the rate of a sublimation and calculate primary drying time.  Propose conditions for shelf temperature and chamber pressure.

3 international Optimum  Definition of Optimum: Superior Drug Quality for the least cost.

4 international Critical Properties  Collapse Temperature (Tc): The temperature above which the frozen product losses its structure and falls (melts) in the freeze-dryer.  Drug stability  Excipient properties  Tg’ and Teu (not critical – used as a substitute for Tc)

5 international Freezing  Purification Step. Water is crystallized out.  Interstitial fluid = freeze concentrate  <1% of the total water may be in the interstitial fluid  The interstitial fluid may contain about 20% water.

6 international Freezing  Interstitial fluid has very concentrated product inferring the following negatives.  Proteins may aggregate  pH may change as salts concentrate  Avoid phosphate, succinate, tartrate  Large increase in ionic strength  Multiple ice – aqueous interfaces  Start with larger protein concentrations – the losses are fixed by amount not percent.  Add surfactants

7 international Cooling Rate  Fast Freezing = small crystals  Slow freezing = large crystals, but it is almost impossible to freeze slowly.  Practical: Freeze at about -1  C / min  Annealing = large crystals, but proteins may be damaged by phase separation or other degradation during the warm period.  Freeze to a temperature below Tc. Wait for product thermocouples to get within 2  C of the shelf set point.

8 international Bulking Agents  Mannitol or Glycine  Mannitol must be crystallized above - 25  C and/or the vial volume must be small.  Mannitol amount > 80% of other constituents will assist in crystallization  Annealing (-20  to -25  C) will assist in crystallization

9 international Primary Drying  Temperature of the Ice is what matters.  Heat must be put in to achieve sublimation  Shelf Temperature “influences” ice temperature  But  Chamber Pressure mostly controls ice temperature

10 international Primary Drying  Select a Target Ice Temperature that is barely less than Tc. To be conservative, lower that by 2  C. Each degree below Tc may prolong primary dry time by ~13% !  When Tg’ (glass transition of active) is lower than Tc, safest temp for stability during freeze drying is <Tg’, but often <Tc will work equally well.

11 international Primary Drying  Chamber pressure needs to be well below the ice vapor pressure at the target temperature.  The product temperature determines (fixes) the ice vapor pressure.  The lowest chamber pressure yields the theoretically fastest sublimation rate. (We will show a proof for this later)

12 international Guidance for a Chamber Pressure Design of Freeze-Drying Processes for Pharmaceuticals: Practical Advice: Xiaolin Tang and Michael J. Pikal Pharmaceutical Research, 21(2): This is an empirical formula that will choose a chamber pressure for you that is between 50 and 300 mtorr. It is hardly better than just choosing 75 or 100 mTorr.

13 international Guidance to Select a Shelf Temp  Shelf temp is greater than Tp by 5 to 40  C  Although it can be mathematically estimated, the collection of input variables makes it nearly as fast to just do an experimental run.  In a development run, raise the shelf temperature until the Tp is achieved.

14 international Ramp to Secondary  Ramp slowly to ambient temperature, 0.1 to 0.15  C, then more rapidly.  Don’t change the vacuum setting, unless it is >200 mTorr. Pressure is inconsequential to desorption.  Heat the shelves hot. Even for proteins shelf temperature can go to 40  to 50  C without damage. Furthermore hot temperature is needed to desorb moisture. Time = 3 to 6 hours at temp.

15 international Clausius Clapeyron 1 Mnemonic attributed to Daniel V Schroeder, Weber State Univ., Ogden Utah Definition of Free Energy An Equation of State

16 international Clausius Clapeyron 2  G =  H -  (T∙S) =  H - T∙  S - S∙  T Derivative of both sides H = E + PV ; Definition (see prior slide)  G =  E + P∙  V + V∙  P - T∙  S - S∙  T Energy is only heat and work.  G =  q rev +  w rev + P∙  V + V∙  P - T∙  S - S∙  T  q rev / T =  S ; Definition of Entropy  G = T∙  S +  w rev + P∙  V + V∙  P - T∙  S - S∙  T  w rev = -P∙  V +  w rev * where the * means all other work  G = T∙  S + -P∙  V +  w rev * + P∙  V + V∙  P - T∙  S - S∙  T Now simplify, and consider only pressure∙volume work.  G = V∙  P - S∙  T  Often a start point for this derivation.

17 international Clausius Clapeyron 3 Since Free Energy doesn’t change between co-existing phases, V s  P - S s  T = V g  P - S g  T (3) rearranging we have (V s - V g )  P = (S s - S g )  T (4) and (5) Clapeyron Now use the definition of entropy to substitute  H/T in place of  S And rearrange

18 international Clausius Clapeyron 4  Clearly, the Volume of Gas is enormous compared to the volume of Solid.  And from the gas law V = n∙R∙T / P 

19 international Clausius Clapeyron 5  Note: “n” is dropped and a prime is added to  H to mean molar enthalpy. Two Point Form

20 international Clausius Clapeyron 6 Now Change P2 to P and express in function form

21 international Clausius Clapeyron 7 R= J/mol∙K T is Absolute in Kelvin P will be in the units of A

22 international Practical Lyo Rates 1  Rate is the weight of liquid removed per unit time.  Often, Rate is the weight of liquid removed per area & unit time.  Sometimes, Rate is the moles of liquid removed per area & unit time.  Happens in Primary.

23 international Practical Lyo Rates 2  Common Units are gm/cm 2 ∙hr  Common Rates are as follows. .02 gm/cm 2 ∙hr  Very Slow Rate .04 gm/cm 2 ∙hr  Medium or Avg. Rate .06 gm/cm 2 ∙hr  Medium to Fast Rate .08 gm/cm 2 ∙hr  Fast

24 international Practical Lyo Rates 3  10 shelves x 12 tray/shelf x 360 vials/tray = 43,200 vials  Vial OD = 22.5mm and glass is 1.2mm thick.  Fill Volume is 2 mL  Total Grams

25 international Practical Lyo Rates 4  Area of 1 Vial Primary Drying took 14 hours to complete.

26 international Vial Sizes

27 international Exercise 5.1: Select a Cycle for a small molecule product with a collapse temperature of -10  C. There will be 25 liters of product (40 mg/mL) and a dose is 20 mg. The fill will be 1 dose/vial. Excipients include only 3mM Glycine for pH control at 4.2. Consider the number of vials and size of the lyophilizer. Select a freezing temperature and time. Select a primary segment chamber pressure Shelf temperature Time in primary Select a secondary segment Shelf temperature & time.

28 international Module 5 Quiz  Participant Directions:  Divide into pairs  Take 5 minutes to complete quiz  Correct answers will be reviewed as a group during debrief

29 international Question 1 of 3  Collapse Temperature for a product has been measured at -41  C. Decision has been made to keep the ice at -43  C.  What is the ice vapor pressure at -43  C?  Why would a lyo cycle developer care?

30 international Question 2 of 3  Use the empirical equation given in the presentation to determine a target chamber pressure for a target temperature of -43  C.

31 international Question 3 of 3 With a 50 mL fill of immunoglobulin in a 60 mL vial (OD = 41.6 mm; wall thickness = 1.6mm) you are asked to set a primary cycle length in hours. The primary segment chamber pressure will be 150 mTorr and the shelf temperature will be +5  C. No further information is available. Pick time in hours to program for primary drying.