* * * INSIGHT * * *
The Importance of Units and Terms in Lyophilization
by
Thomas A. Jennings, Ph.D.
Those entering the field of lyophilization often write to me and express how difficult it is to obtain a grasp of the subject. Part of the problem lies in the complexity of the subject and another is in the diversity of units and terminology which just adds to the confusion. It is hoped that the Standards Committee of the ISL-FD Inc., under the able Chairperson leadership of Larry Ulfik, will in time resolve this problem by obtaining from the membership an agreement on a standard set of units and terminology. Those working in the field of lyophilization come from many countries and speak many languages but the units and terminology should be global in nature.
I felt the best way to address this issue is to review a paper recently published by T.W. Randolp and J.A. Searles [1] with respect to the use of units and terminology in preparing a paper in this field. I have been in contact with one of the authors (JAS) and he is well aware of my concerns about this paper and has been kind enough provide me with additional information. I think it only fair to point out that I using this paper only because it seems to typify many other papers written in this field and it is not meant by any means to embarrass or discredit the authors. I have no doubts that I have in the past been guilty of not clearly defining expression or terms so I am certainly not without fault. But still, I feel that it needs to be said that in order for us to advance the science and technology of lyophilization or freeze drying we must find common grounds upon which to work. It is therefore the objective of this INSIGHT to attempt to examine the above mentioned paper [1] through the eyes of a Novice just entering the field of science.
Units: As a Novice I am grateful to authors for outlining the general steps in the lyophilization process and I find the description of the freezing process to be very informative. I can understand the removal of the ice by sublimation at temperatures well below 0 oC, i.e., -20 oC to -45 oC and at pressures ranging from 10-4 to 10-5 atmospheres. However, the gauge on the freeze dryer that I am using indicates pressure in units of mTorr or microbars. So what is the actual pressure range I can expect to operate in my dryer? Making the pressure conversations I find that 1 x 10-4 atmospheres is equivalent to 76 mTorr or 100 microbar and at 1 x 10-5 atmospheres. The pressure is about 8 mTorr or 10 microbars. So as a Novice I am left with the impression that the primary drying will be done at pressures well below 100 mTorr or 133 microbars. But I am now confused for I read that other authors may have performed their primary drying at temperatures of -28 oC but at pressures greater than 100 mTorr [2]. The problem here is that I think that it was the good intentions of the authors to give the reader some general idea of the pressure ranges involved in the process but in doing so may have, in cases like our Novice, may have caused some confusion. I have been in the field of lyophilization for some number of years and the only time I have came across a primary drying process that was being conducted at 8 mTorr was when there was an error in the accuracy of the gauge. It is therefore recommended that in the future that when giving ranges of pressures one should use currently accepted units.
The Standards Committee has issued a report to the Society membership recommending that Pascals be used as the standard pressure unit in reporting data regarding the lyophilization process. It will take some time for some of us get use to Pascals so the pressure data will for a number of years be report as Pascals (mTorr or microbar). But the end result is that in just a few years everyone will be describing their processes in a common pressure unit.
Continuing to read further the Novice is next confused that after sublimating all the ice from the sample, there still remains 30% water. The Novice may think the authors are referring to 30% wt/vol., whereas, the more experienced authors have assumed that everyone knows that they are referring to 30% wt/wt. For the Novice, 30% wt/vol. would imply that for a 1 mL fill volume there would still be about 300 mg of water remaining in the product while for the authors a 1 mL fill volume, having a solid content of 10 mg, the amount of water remaining would be just 3 mg. As a result, authors must be rigorous in using units to avoid any such misunderstandings.
The authors in the following equation offer a simplified expression for determining the sublimation rate of ice from the product. Admittedly they ignore any heat transfer resulting from convection and radiation in order to simplify the model and, in my mind, this is quite acceptable. Their resulting expression is as follows
Sublimation rate = dm/dt = Q/DHs = [kh Av (Tshelf - Tproduct )]/DHs (1)
In the paper the authors define the terms of the above expression as follows
dm/dt = rate of change of mass due to sublimation
Q is the heat that flows to the sample
DHs = heat of sublimation
kh Av = product of the heat transfer coefficient and the effective surface area of the vial in contact with the shelf.
To the Novice dm/dt is fairly obvious and would have the units of mass/time. In addition, he has no trouble that Tshelf and Tproduct must infer temperatures expressed in oC; however, he is less certain of the units in remaining terms. Because one of the authors (JAS) is a member of the ILS-FD, Inc., the Novice was able to contact this author and the author was kind enough to provide him with the units of the remaining terms for expression (1).
Q = joules (J)/sec.
DHs = J/gram
kh = J/sec/m2/oC
Av = m2
Examination of expression (1) now shows that Q/DHs and [kh Av (Tshelf - Tproduct )]/DHs will both have units of g/sec.
The Novice is now introduced to a second expression for the sublimation rate which is given as
Sublimation rate = dm/dt = (Pproduct - Pchamber )/ (Rproduct + Rsystem) (2)
where
Pproduct is the vapor pressure of the ice at the sublimating front,
Pchamber is the pressure in the chamber
Rproduct is resistance of the water vapor flow through the cake
Rsystem is the resistance of the mass transfer of water vapor from the surface of the product to the condenser.
Now our Novice knows that for a given temperature the ice will have a vapor pressure of water. He also knows that the chamber pressure will be ranging between 10-4 to 10-5 atmospheres. But he has no idea of the units for the resistance terms so once again the author (JAS) comes to his aid by providing the units
R = sec mTorr/g
P = mTorr
The Novice is now pleased because the pressure units are those he uses on a daily basis.
The Novice proceeds to read further and comes across a third expression
log Pproduct = A - B/(C + Tproduct ) (3)
and reads that the terms A, B and C are empirical constants.
The authors now equate expressions (1) and (2) and substitute the value for Pproduct from expression (3) to obtain a final expression
[kh Av/ DHs (Tshelf - Tproduct)] =
[10 [A - B/(C + Tproduct)] - Pchamber )/ (Rproduct + Rsystem) (4)
The Novice knows that the term [A - B/(C + Tproduct )] is now being used as an exponent and therefore the constants B and C must have the units of oC. Thus in expression (4) he can substitute the numerical term D for 10 [A - B/(C + Tproduct)] where D has no units.
The authors state that from expression (4) one can now solve for Tshelf. Solving expression (4) for Tshelf, the Novice obtains the following expression
Tshelf = Tproduct + DHs/ kh Av [ D - Pchamber )/ (Rproduct + Rsystem) (5)
or
Tshelf = Tproduct + DHs D / kh Av (Rproduct + Rsystem)
- DHs Pchamber / kh Av (Rproduct + Rsystem) (6)
Solving equation (6) in terms of units the Novice finds that
oC = oC + oC/mTorr - oC(7)
and since the units on the left hand side of the equation do not agree with those on the right hand side, one cannot use expression (4), as it is presently written, to determine Tshelf.
The authors could have clarified expression (4) for the Novice had they defined Pproduct as follows:
Pproduct = Np x (1 mTorr) or Np x (1 pressure unit) (8)
where Np = numerical value of the pressure.
Thus equation (4) now become
[kh Av/ DHs (Tshelf - Tproduct)] = [10 [A - B/(C + Tproduct)] x (1 pressure unit)
- Pchamber )/ (Rproduct + Rsystem) (9)
Now when the Novice checks the units for determining the shelf temperature he finds that the units on the left hand side of equation (7) now agree with those on the right hand side.
I do not believe for one moment that the authors meant to confuse the Novice and perhaps assumed that everyone looking at equation (4) would have understood that pressure units were implied; however, use of equations (8) and (9) prevent any misunderstanding of their intent. It is unfortunate but equation (4) in its literal form is incorrect and does misrepresent the intent of the authors.
With the aid of equation (9) the Novice is delighted with the thought of being able to determine Tshelf but then is soon discouraged for he still must determine the values of DHs, kh, Av and (Rproduct + Rsystem). The authors give a reference for determining (Rproduct + Rsystem) but not DHs, kh and Av so our Novice still has no means for determining Tshelf . So the only real value that the Novice can obtain from reading this paper thus far is that controlling the primary drying is indeed a very complex process and there are many factors to take into account.
It would be easy to cast total blame on the authors for not being more diligent in preparing the paper. But in my opinion, diligence also should have been exercised on the part of the experts who reviewed this paper and approved it for publication. If the reviewers had been more diligent, they would have seen what the Novice found when he read the paper. If the reviewers had pointed out the those concerns to the authors, the authors would have no doubt been very grateful and the resulting revised paper would have proven much more helpful to the Novice.
Terms: The authors explain to the Novice that the energy for the sublimation process stems from the “cooling” fluid that circulates through the shelves, That would mean that in order to apply heat to the product one would have to heat the “cooling” fluid. The authors then proceed to present expression (1) where the term Tshelf is used. If the Novice has read INSIGHT Vol. 1 No. 7, then he is not sure if the authors are referring to the shelf fluid temperature (which is often the case) or are they making reference to the shelf surface temperature because the term Av represents the surface area of the vial that is in contact with the shelf. So the Novice is not quite certain as to the exact meaning of Tshelf.
Another term that puzzles the Novice is the use of resistance (R) to represent the flow of gas through the cake and vacuum system. He happens to be familiar with the classic text on vacuum technology by Dushman [3] in which gas flow (G) is expressed in terms of conductance (F) of the system. Thus G can be simply expressed as
G = F (P1 - P2) Pressure Volume/Time (8)
where (P1 - P2) represents the difference in pressure across the system and F has the units of volume/ time. When using expression (8) The Novice is aware of the fact that the expression for the conductance (F) will change with the nature of the gas flow (see INSIGHT Vol. 1 No. 4). The authors do address this issue, although they refer it to the Knudsen diffusion. where the pore size of the cake plays an important role in determining the nature of the gas flow.
For the conductance F, where the pore size of the cake plays an important role in determining the nature of the gas flow. For example, at a given value of (P1 - P2) but for a cake structure comprised of very fine pores the gas flow may be molecular in nature, i.e., that the number gas-wall collisions far exceeds the number of gas-gas collisions. For molecular flow the expression for the conductance is given as Fm and found to be independent of the mean-free-path of the gas. However, if the pore sizes are large enough that the gas flow is viscous is nature then the number of gas-gas collisions will far exceed the number of gas-wall collisions and the gas flow is considered to be viscous in nature. For viscous flow, the expression for the conductance will be Fv and inversely proportional to the means-free-path of the gas. The gas flow from a cake under viscous flow Gv will exceed the gas flow under molecular flow Gm because Fv > Fm for the same (P1 - P2). The remaining portion of the paper [1] considers means for controlling the size of the ice crystals which would indeed affect the nature of the gas flow and for that reason it is well worth reading.
But then the Novice examines the Rproduct which has the units of (time pressure)/mass. The Novice must assume that the mass refers to the mass of gas flowing through the cake while the pressure term is defined by the authors as the pressure differential from the sublimation surface to the top of the cake. The Novice can understand that as the pressure term increases it will result of an increase in Rproduct. However, the mass will be depended on the temperature at the sublimating interface. A decrease in the temperature of the ice at the sublimating interface will result in a decrease in the sublimation rate and a decrease in the mass term and for a given Rproduct will result in an increase in time. However, the use of the term Rproduct does not provide the bases for understanding of the role that the pore structure of the cake will have on the gas flow because the nature of the gas flow will be dependent on the expression used in defining the conductance term (F).
Summary: It is hoped that future authors of papers on lyophilization or freeze drying will pay closer attention to units when using terms and mathematical expressions. Authors should keep in mind that many who read their paper may be Novices in the field and what may be obvious to them may not be obvious to a Novice.
Authors should be careful not to use ambiguous terms that could confuse the reader. Authors should avoid creating terms when there are already well accepted terms that can provide a sound foundation for our understanding of this complex process called lyophilization. We should by all means encourage new concepts when it provides a significant addition to our total knowledge.
Reviewers of papers need to be more diligent when reviewing a paper. They must change their judgmental approach to one of assistance to authors in order to strengthen the final publication.
Finally, all of us interested in advancing the science and technology of lyophilization should close ranks and support efforts of the Standards Committee of the ISL-FD Inc. so that, although we may speak different national languages, we will all share a common understanding of the units and term used in this process. The Standards Committee is open to all who wish to participate and everyone is free to express their views. A very active Standards Committee can be a big step in fulfilling our mission.
Acknowledgment:
I would like to extend my warm thanks to the author Dr. James A. Searles for bearing with me and providing me units for the various terms used in this INSIGHT. I will certainly welcome any comments that the authors or any one else may wish to make concerning this INSIGHT and publish it on the web site provided such a response is rendered in a professional manner.
References:
1. T. W. Randolph and J. A. Searles, “Freezing and Annealing Phenomena in Lyophilization: Effects Upon Primary Drying Rate, Morphology and Heterogeneity” in American Pharmaceutical Review, Vol. 5 Issue 4, pp. 40 - 46 (2002).
2. T. A. Jennings, Lyophilization - Introduction and Basic Principles, Interpharm Press, Buffalo Grove, IL 1999.
3. S. Dushman, Scientific Foundations of Vacuum Technique (J. M. Lafferty, ed.) Second Edition, John Whiley & Sons, Inc. New York 1962.
Vol. 6 No. 2. February 2003
