# F0 Value in Steam Sterilization

Any sterilization technique including the F0 value is intended for microbial reduction to the pre-determined levels.

Sterilization helps to maintain the safety, quality, sterility, and integrity of the pharmaceutical product.

Various sterilization techniques practiced in healthcare facilities or life-science industries based on the type of application.

Out of that, the F0 value (read as F Zero) designed in the industrial field of moist heat sterilization.

Before detailing the F0 value and its significance, it is important to understand the kinetics of moist heat and its mathematical versus biological angle.

Page Contents

## Moist Heat Kinetics (Math vs. Bio)

Assume a microbial species that has contaminated the system is in contact with saturated steam at a constant temperature.

Therefore, sterilization develops like a first-order chemical reaction. Then, the rate of the reaction can be written out mathematically as;

Where,

N – Number of microbes present in the system

t – exposure time to the microbes with steam

K – the rate of reaction’s constant (**species dependent**)

Re-arranging to integrate,

Now integrating,

Converting and simplifying the logarithmic value to exponential,

where,

N_{0} – no. of microbes initially

t – exposure time of steam (sterile hold time)

N – no. of microbes at the end of sterilization hold

k – the rate of reaction constant (microbes dependent); now this k = K / 2.303. Here, **K is called the Death Rate constant**.

The equation (1) hence shows that no. of microbes decreases exponentially with sterilization hold time.

Also, the time required to decrease the microbial amount to a pre-defined

### What is D-Value (Decimal Decay Time)?

D-value is the time (t) required at a specified temperature (T) to reduce the microbial population from 100% to 10% (1 log reduction).

Definition of D-value

Mathematically, the D-value is the reciprocal of rate of reaction constant (k) and therefore;

K = t^{ -1}

By putting this value in earlier equation (1) we get,

N = 0.1*(N_{0})

The D-value plays an important role in determining hold time for the system under the sterilization.

Equally important, D-value is considered as “1” if there is no precise experimental data available. Typically, the range for D-value is 0 to 2 min. at around 121°C.

Therefore, in simple terms, D-value is the time required in minutes to destroy the 90% population of the micro-organisms.

**D-Value vs. Time**

Let us understand the importance of D-value with an example where we want to reduce micro-organisms with moist heat sterilization.

- Initial no. of microbes = 100 i.e. 10
^{2} - Target reduction of microbes = 10
^{-6} - Constant Temperature of sterilization process (T) = 121°C

Table below represents figures based on an experimental data, which elaborates how the D-value affects microbial reduction time:

D-Value (min.) | Time Required for Microbial Reduction (min) | Initial No. of Micro-organisms | Final No. of Micro-organisms |
---|---|---|---|

0.5 | 4 | 100 | 10^{-6} |

1 | 8 | 100 | 10^{-6} |

2 | 16 | 100 | 10^{-6} |

**Table: D-value vs. Time required for microbial reduction**

Summarizing the above table, it shows that residual contamination of 10^{-6} is gained from initial contamination of 10^{2} at 121°C in

- 8 mins if D
_{121}=1, - 4 mins if D
_{121}=0.5 and - 16 mins if D
_{121}=2.

Another way to calculate the D-value is by using the following formula.

**D = t / (logC _{o} – logC**)

where, t – exposure time in minutes

C_{o} – initial number of micro-organisms

C – final number of micro-organisms

Please remember the log values we’re discussing are log_{10} and not log_{e}.

For these numbers to understand, European Pharmacopeia introduced a concept called SAL (i.e. **Sterility Assurance Level**). SAL is the probability of identifying a non-sterile unit or micro-organism in a batch or lot.

According to the Table above, SAL=100 and 10^{-6}. Therefore, the probability of identifying non- sterile microbe is one in 100 and one in a million, respectively.

### What is z-Value (Temperature Coefficient)?

Practically speaking, the t

The z-value is used to correlate the heat resistance of the micro-organisms to changing temperature.

Let us define the z-value.

z-value is the number of degrees the temperature is required to be increased which will effect a 10-fold variation of D-value.

Definition of Z-Value

The z-value is considered as 10°C for the temperature range from 100 to 130°C for steam sterilization. Generally, bacteria that forms spores have a z-value ranging between 10 to 15°C while the non-spore-forming ranges in between 4 to 6°C.

Approximately D-value varies by 10 times for variation of 10°C. Again, this must not be interpreted that D-value varies by 1 time for 1°C variation.

The rationale for this is beyond the scope of this topic. To keep things simple, only note that “**Variation in 1°C requires a variation of D-value by around 25%-30%**”.

The effect of temperature variation decreases considerably upon:

1. Changing the sterilization method

2. Raising the temperature

For example, for dry heat sterilization of around 200°C, the

At 121.1°C, practically no microbe has precise D=1 min and z=10°C but the combined application of these two parameters to calculate F0 value provides a sufficient margin of error.

Summarizing the earlier dialogues, D-value has a unit of time i.e. min and z-value is a temperature coefficient and has a unit of temperature i.e. °C.

The upcoming part describes how the D-value and z-value help to draw a meaningful outcome for the effectiveness of sterilization i.e. F0 value.

## F0 Value (Equivalent Exposure Time)

F0 value is the equivalent exposure time at 121.1°C to that of the actual exposure time at a variable temperature calculated with a temperature coefficient of the destruction of 10°C.

F0 Value Definition

where,

Δt – the time interval between two temperature readings

T – the temperature at time t of the product under sterilization

z – temperature coefficient (assumed as 10°C)

The term next to Δt is called Lethality Rate. You can calculate it individually or by averaging all the tabulated data, the result will be equivalent.

### Testing F0 Value And Its Meaning

Consider sterilization hold time of 30 min. at constant 121.1°C, putting this in equation (2),

Solving we get, F0 = 30 min. (*This is an ideal cycle/condition for steam sterilization*)

Based on this, let’s see two further examples one below and one above ideal condition.

#### Example 1 (Below Ideal Condition)

Consider sterilization hold time of 30 min. at constant 110°C instead of 121.1°C, in a similar manner as above,

Solving we get, F0=2.33 min.

Hence, a 30 min. of sterilization at 110°C is lethally equivalent to 2.33 min. of sterilization at 121.1°C. *(Compare this sentence with the definition of F0 value for easy understanding)*

The crux of the example is,

121.1°C **→** 30 min. (Expected condition)

110°C **→** 2.33 min. (Actual condition compared to the expected condition)

Therefore, according to the expected condition; the effective sterilization cycle time was only 2.33 min. instead of 30 min. because of the lowered temperature of 110°C.

Let’s understand “how long will it take to complete the sterilization?” According to the above example, if we maintain temperature 110°C constantly, how much hold time required to achieve F0 value of 30 min.

By reverse calculation, we can do this. Let’s fix the F0 value to 30 min. The unknown part then would be Δt.

We have the following data with us:

F0=30 min.

Temperature T=110°C

Putting these values in equation (2),

Solving we get, Δt=386 min.

**When the temperature of the system under sterilization maintained at a constant 110°C, the time of 386 min. (i.e. Sterile Hold Time) would be required to achieve the lethal effect of 121.1°C at 30 min.**

#### Example 2 (Above Ideal Condition)

Consider sterilization hold time of 30 min. at constant 125°C instead of 121.1°C, in a similar manner as above,

Solving we get, F0=73.64 min.

Hence, a 30 min. of sterilization at 125°C is lethally equivalent to 73.64 min. of sterilization at 121.1°C. *(Compare this sentence with the definition of F0 value for easy understanding)*

Simply put,

121.1°C **→** 30 min. (Expected condition)

125°C ** →** 73.64 min. (Actual condition compared to the expected condition)

Therefore, according to the expected condition; the effective sterilization cycle time was 73.64 min. instead of 30 min. because of the raised temperature of 125°C.

Let’s understand “how long will it take to complete the sterilization?” According to the above example, if we maintain temperature 125°C constantly, how much hold time required to achieve F0 value of 30 min.

By reverse calculation, we can do this. Let’s fix the F0 value to 30 min. The unknown part then would be Δt.

We have the following data with us:

F0=30 min.

Temperature T=125°C

Putting these values in equation (2),

Solving we get, Δt = 12.24 min.

**When the temperature of the system under sterilization maintained at a constant 125°C, the time of 12.24 min (i.e. Sterile Hold Time) would be required to achieve the lethal effect of 121.1°C at 30 min. **

## Conclusion

F0 value provides lethal equivalence between expected and practical conditions. Taking notes on practical values of lethal doses, D-value and z-value become very important while evaluating F0 value precisely.

When the average temperature of the system is below the set value of 121.1°C, the sterilization cycle may lead to failure even if the sterile hold time completes. Ultimately because not bringing out a residual reduction of micro-organisms.

When the average temperature of the system is above the set value of 121.1°C, the sterilization may be lethally equivalent even before the set sterile hold time.

**Note:** This lethal equivalence has technical value only when the steam used for sterilization is **Saturated**. Otherwise, this equivalence is pointless.

F0 value calculation can be done either post sterilization or in real-time depending upon the chosen method.

The ‘post sterilization’ approach helps in analyzing and evaluating the lethal equivalence once the cycle has finished.

While real-time calculation during sterilization with a suitable controller will help in controlling the sterilization cycle till it achieves the preset F0 value.

Most of the pharmaceutical companies practicing steam sterilization rely on the calculation of F0 value for analysis purposes.

Though the logic-based controllers are capable to effectively drive the sterilization cycles based on the F0 value hassle-free.

This article was mainly focused to enlighten the concept of F0 value in a systematic breakdown.

Read these articles to dig deep into further developments on the F0 value.

1. F0 Value and Sterilization Cycle Development

2. How Steam Quality has a significant impact on Sterilization?

3. F0 Value Calculator

Also, this is an interesting article on the validation approach for the steam sterilization process in autoclaves.

## F0-value: FAQs

### What is f0 value?

F0 value is an equivalent exposure time at 121.1°C to that of the actual exposure time at a different temperature calculated with a temperature coefficient z-value of 10°C. Read more in the above article.

### How do you calculate f0 value in autoclave?

To calculate the F0 value, average the temperature of each probe during the sterile hold and then average the different temperatures to get one single temperature. Use the formula shown in the above article to estimate the F0 value.

### What is D value and Z value?

D-value is the time (t) required at a specified temperature (T) to reduce the microbial population from 100% to 10% (1 log reduction). z-value is the number of degrees the temperature required to increase, which will effect a 10-fold variation of D-value.

This article clearly explains the significance of F0 value in steam sterilization.Thanks for explaining it clearly.

Hey Nikki! Glad that this added value to your know-how. More such content in pipeline. Stay tuned and take care 🙂

Because of examples, it was easy to understand D, Z and F0 value concept.

Hey Manisha! Thanks for that and wish you all the best!

Hi Saket. I found this article via LinkedIn. I am very impressed with the quality of the write-up. It is pretty easy to understand at the same time informative.

Hey Ranjeet! Thank you for your words and wish you all the best. Keep in touch.