The following simplified summary may be used to explain these concepts in an easily understood manner to those who may be less trained, but who would nevertheless benefit from grasping the essence of the work they are performing.

An attempt has therefore been made to make this explanation:

• easily understandable; mathematical expressions and abstract concepts have therefore been minimized
• short; only the most important concepts and parameters have therefore been dealt with.

This has naturally limited the completeness and rigor of the description.

NOTE: The term unit defines a physically delimited system within which microorganisms can "homogenate" and proliferate
A bottle or vial, together with their contents, are a unit.
It is more difficult but equally necessary to extend the concept of unit to a container which contains for example a filtering system or a certain mass of clothing.

1. Up to just a few years ago, steam sterilisation was thought to be a "potential-barrier", i.e. "all-or-nothing" , phenomenon.
   This would mean that once a certain temperature is reached and maintained for a certain time, all the microorganisms contained in a unit die within that time, regardless of their number. The risks of such an assumption are evident.
2. Nowadays, it has been shown that steam sterilisation instead proceeds like a first-order chemical reaction and therefore at a specific rate which is higher as the temperature rises and is a function of the number of microorganism present in the unit.
3. This rate can be expressed by means of the decadal (or decimal) decay time, indicated by the symbol D.
4. D is the time, in minutes, required to reduce the number of microorganisms present in the unit to one tenth.
5. D varies according to the kind of microorganism (and to its "history"), the medium in which it is immersed and, as mentioned, the sterilisation temperature.
6. At the temperature of 121°C, D is comprised between 0.5 and 2 minutes: for microorganisms commonly dealt with we can assume, as an average, that D = 1 minute.
7. This means that at the end of each minute of permanence at 121°C the number of microorganisms reduces to one tenth of the number at the beginning of that minute.
8. Therefore, if a unit is kept at 121°C for 3 minutes, the number of microorganisms contained therein is reduced to one thousand (1/10 x 1/10 x 1/10 = 1/1,000) of the initial number.
9. If the initial bacterial load of a batch of units being sterilised is on the average 1,000 (i.e. 1,000 microorganisms per vial or bottle), after 3 minutes of treatment at 121°C it is reduced on the average to 1, following this progression.

    

10. After a further minute of sterilisation (4 minutes altogether) this reasoning leads one to the conclusion that the load has dropped to 1/10, i.e. 0.1. However, this must be understood to mean that at this point each unit contains one tenth of microorganism (in which case the units would be sterile...) but must be taken to mean that there is a probability that 1/10 of the units are still contaminated.
11. After 9 minutes of treatment at 121°C, the bacterial load of the batch at issue is reduced, on the average, to 1/1,000,000, i.e. 10^-6. The probability of still having a contaminated unit in that batch is therefore 1 in 1,000,000.
12. This is the minimum assurance of sterilisation which must be achieved in pharmaceutical field, thought a grater assurance, for example 10^-9, i.e. 1 in 1 billion, is often sought.
13. This assurance is expressed a PNSU, i.e. Probability of Non Sterile Unit.
    PNSU = 10 ^-6 means that the probability of finding a non-sterile unit in the batch is 1 in 1 million.
14. In order to achieve a given PNSU it is necessary to meet several conditions:

• to statistically know the initial bacterial load of the batch (which is anything but easy to determine)
• to be certain that even the coldest point inside the units of the batch has received a lethal heat dose sufficient to obtain the required PNSU
• if sterilisation at 121°C is not performed, to be capable of relating to 121°C (by calculation) the effectiveness of sterilisation in order to correctly apply the previously defined concept of D.

1. F₀ is defined as:

• the time during which sterilisation is actually performed at 121°C, or
• the time during which sterilisation is performed at another temperature, related by calculation to 121°C so as to be equivalent in terms of lethal heat dose, i.e. of microbial destruction effectiveness.

NOTE:
The exact reference temperature of F₀ is 121.11°C, as this value corresponds to 250°F

1. The "overkill", i.e. "over-sterilisation", approach is generally used when a sterilisation process for heat-sensitive products is validated.
   Essentially, with this approach it is necessary to provide an F₀ which is safely and routinely not lower than 12 (and indeed has a good safety margin with respect to this minimum value) exclusively during the sterilisation phase (i.e. ignoring the lethal heat doses provided during heating and cooling) to the unit placed in the coldest point of the load.
2. In practice, it is conceptually easy and relatively trouble-free to relate by calculation the sterilisation time to 121°C or F₀after the process.
   On the contrary, this is difficult to do do in "real time", i.e. while sterilisation is in progress, since the calculation must be performed so quickly that the use of a computer is unavoidable.
3. Due to the above it is now clear and evident that if F₀ = 12 is to be achieved, the required sterilisation time is lower than 12 minutes if the sterilisation temperature is greater than 121°C and longer than 12 minutes if the temperature is lower than 121°C.
4. Let us now try to quantity that "lower" and "higher" than 12 minutes.
   For most of the microorganisms with which we commonly deal, it is assumed that every 10°C of shift from the temperature of 121°C entail a tenfold variation in the sterilisation rate.
5. Therefore, if we work at 111°C, in order to achieve an F₀ equal to 12 it is necessary to sterilise for 12 x 10 = 120 minutes, whereas if we work at 131°C then 12/10 = 1.2 minutes, i.e. 72 seconds, are sufficient.
6. If we want to determine the extent by which the sterilisation rate varies for temperature variations of 1°C we must find the number which yields 10 when raised to the tenth power. This number is 1.2589: 1.2589 multiplied by itself 10 times gives 10.   (actual 102589254118 to 9 sig figs)
   This means that a 1°C variation in the sterilisation temperature causes an increase (or reduction) of the sterilisation rate by a factor of 1.2589, i.e. 25.89%.
7. Similarly, it can be shown that a temperature variation of 0.1°C causes a rate variation with a ratio of 1 —> 1.02, i.e. approximately 2%.
8. It is therefore evident that even small temperature variations around 121°C cause highly significant and hardly negligible variations in the sterilisation rate.
   For example, sterilizing at 119°C in fact means increasing (approximately) the sterilisation time by 1.2 x 1.2589 x 1.02 = 1.54 times to relate it to 121°C.
   Therefore, for example, if F₀ = 12 is to be achieved, it is necessary to sterilise for 18'45'' instead of 12'.
9. The following mathematical expression allows the calculation of F₀ and is provided merely for information:

   where T is the actual temperature at the time being considered, and the number at the denominator of the exponent is the value of z, which is always assumed equal to 10 in the expression of F₀.

10. Since it is an exponential expression, the calculation of F₀ is not very fast.
    This is why a Lethal Ratio table has been compiled with allows to pass, by means of a simple multiplication, from any sterilisation time at a certain temperature to F₀ for temperatures between 90 and 130.9°C with intervals of 0.1°C.
11. The above mentioned table is Enclosure 4. Choose the temperature, in whole centigrade degrees, in the left column and the tenths of degree to be added in the top row. The intersection of the two values yields the required ratio.
    For example, the ratio framed with thin lines is for 120.0°C, the dotted Ratio is for 120.2°C and the thick-framed ratio is for 121.8°C
    The ratio for 121.1°C is naturally approximately 1 (it would be exactly 1 for 121.11°C).
12. Therefore, if we refer to the factor for 120.0°C we can say that any sterilisation time at 120.0°C must be multiplied by 0.774 to make it equal to the time at 121.1°C, i.e. to express it as F₀.
    
    

    Therefore	1 minute at 120.0°C=	1' x0.774=0.774 minutes at 121.1°C
    	15 minutes at 120.0°C=	15' x0.774=11.61 minutes at 121.1°C
    	20.5 minutes at 120.0°C=	20.5'x0.774=15.87 minutes at 121.1°C

     

    NOTE
    The decimals of the time values are tenths and hundredths of a minute, not seconds.

13. If a calculation of F₀ after the process is to be performed on the basis of a chart of the temperature taken inside a unit subjected to sterilisation, it is possible to operate as described in graph 1.

14. The diagram of Enclosure 5 is an illustration, in somewhat comic-book style, of the concepts of F₀, D and PNSU.
    Graph 1