Process Dynamics of EtO Sterilization

Originally Published MDDI March 2003Sterilization

March 1, 2003

14 Min Read
Process Dynamics of EtO Sterilization

Originally Published MDDI March 2003


A mathematical model that uses microwave spectroscopic methods to interpret EtO measurements may provide a powerful software tool for process engineers.

by Zhangwu Zhu and Ian P. Matthews

The direct analysis of water vapor and ethylene oxide (EtO) gas during EtO sterilization for parametric release has become a routine practice. This has been made possible by the development of microwave spectroscopic technology.1,2 This technology has also enabled the detailed study of the dynamics of EtO sterilization processes with differing parameters. 

Microwave Spectrometry
Reports of the R&D efforts involving a microwave spectrometer provide detailed explanations of the instrument's design and operation.3–10 The inherent advantages of microwave spectrometry meet the essential requirements for monitoring an EtO sterilization process. This is because the technique is highly specific, with no cross-contamination of the measurement by the presence of other gases. This technique is also highly accurate (typically in the range of 1.5% standard deviation in the calibration range 0 to 100%). In addition, the technique is highly robust and reliable.

In a typical installation, the gas sample is taken in real time from the chamber's recirculation line, so that the spectrometer measurement represents real-time concentrations of EtO gas and water vapor in the chamber headspace (i.e., the void space around the load). 

A mathematical model has been developed to correlate measurement data representing the headspace and process parameters (pressure, temperature, and load dimensions and density) to the process dynamics (i.e., the real-time concentration distributions and sorption/desorption of gas and vapor within the load space). 

Mathematical Modelling

The gas/vapor distribution within the load in the chamber is assumed to be consistent with the diffusion equations: where C is the gas/vapor concentration, t is the time, 2 is the spatial partial differential operator, S is the sorption of the gas/vapor molecules into the load, and D, ks, and kd are the rate coefficients:

D = diffusion coefficient,
ks = sorption coefficient, and
kd = desorption coefficient.2,3

The first term on the right-hand side of Equation 1 represents gas/vapor diffusion due to the spatial concentration gradient. As gas/vapor diffusion proceeds into the load, the EtO and water molecules will be immobilized by the load materials. These are subsequently mobilized during the post-sterilization aeration phases. These processes are known as sorption and desorption, and their effect on the concentration distribution in gas phase is the second term in Equation 1. The buildup of sorption in the load can be separately described by Equation 2. 

It is assumed that the ideal-gas law applies to the gas phase (the headspace and the void spaces inside the load) within the chamber.
For ease of mathematical solution, the load is considered to be a symmetrical shape, such as a sphere or a long cylinder. This allows the three-dimensional equations to be reduced to a one-dimensional equation of one coordinate of radius, r.

Figure 1. Display window containing diagrams (a1)–(d1) for cycle 1. (Click to enlarge).

The Diffusion Process

It should be mentioned that all data reported in this article are presented in a display window format as seen in Figures 1–7. There are four diagrams in each window. The diagram on the top left (labeled as ax, where x = 1, 2, … to represent different time events) shows the cycle pressure/time diagram and EtO concentrations in milligram per liter, as measured by the spectrometer. The diagrams on the top right (labeled as bx) and bottom right (labeled as dx) display the EtO concentration distribution in the load headspace and void spaces, with depth in milligram per liter and percent, respectively. The diagram on the bottom left (labeled as cx) shows the EtO concentration in milligram per liter sorbed into load material with depth.

Above each diagram are several text boxes. Above the diagram of ax are boxes labeled Cycle Phase (which shows evacuation in cyan, nitrogen in solid green, air in dotted green, steam in blue, and EtO in red), Pres. (showing pressure in inches or mercury absolute), and Temp. (temperature in Farenheit). Above the diagrams of bx and cx are Integrated mg/L (averaged EtO concentration with depth), Center (EtO concentration at the center of the load), and Surface (EtO concentration on the surface of the load). Above the diagram of dx are Center (EtO concentration at the center of the load) and Surface (EtO concentration on the surface of the load).

The authors studied two different cycles. The data from cycle 1 are shown in Figures 1–5. Different time events are labeled by ax, bx, cx, and dx (where x = 1–5). The data from cycle 2 are compared in Figures 6 and 7, representing two different time events.

Figure 1(a1) shows EtO gas injected during the gas and dwell phase (identified in red) into the headspace, which is under constant recirculation by a blower. As a result, the EtO gas distribution in the headspace is considered to be uniform. Because the diffusion on the boundary between the load and headspace is continuous, the headspace concentration is considered to be the same as that on the load surface. 

Figure 2. Display window containing diagrams (a2)–(d2) for cycle 1. (Click to enlarge).

As shown in Figure 1(b1), as injection proceeds, the EtO gas penetrates the load as a result of the forces of surface-to-center pressure gradient and molecular diffusion. The time interval is 1 minute. The initial chamber pressure and the load density determine the penetration rate. The lower the initial pressure and density, the faster the penetration. 

The dynamics of this process can also be seen in the spectrometer data (displayed by small circles in Figure 1(a1)), which overshoots at the end of gas injection and gradually decreases, approaching the target level, shown as dotted lines in Figure 1(a1) and (b1). The chamber initial pressure determines the overshoot height. The higher the chamber initial pressure, the higher the height of overshoot. The load density determines the rate of the headspace concentration approaching equilibrium. The lower the density, the higher the rate (i.e., the higher the diffusion coefficient D). In other words, the lower the density, the more rapidly the concentration penetrates to the center of the load, which is considered to be the most challenging location for quality assurance of sterility. The spectrometer data are used to determine the diffusion coefficient D.

In a conventional cycle, such as cycle 1 shown in Figures 1–5, the chamber pressure is maintained during the gas dwell phase by "makeup," which is the addition of EtO gas to the headspace (shown in red in Figure 2(a2)) as pressure drops below the lower limit of the dwell window. This is done to restore the pressure to the upper limit of the window. In this case, the EtO concentration is highest at the surface of the load and lowest at the center throughout the dwell phase. 

Figure 3. Display window containing diagrams (a3)–(d3) for cycle 1.  (Click to enlarge).

Concern about inadequate sterility at the center, especially in the cases of high-density loads, may result in the design of cycles that have an excessively long gas dwell time and use large amounts of gas. This would in turn increase the problem of poststerilization residues and prolong the release time.

The above cycle can be modified (to cycle 2, as shown in Figures 6 and 7) so that at the beginning of the dwell, a nitrogen overlay, or N2 blanket, is added to the headspace. This is shown in Figure 6(a1). This dynamically generates a greater surface-to-center pressure gradient and shifts the highest concentration from the surface towards the inside of the load. This then assists EtO gas penetration into the center, as demonstrated in Figure 6(b1). 

In this case, as shown in Figure 6(a1) and (b1), 36 minutes were required from the start of the dwell for the center concentration to reach a predetermined value, say 300 mg/L, as opposed to 66 minutes in the previous case (see Figure 1(a1) and (b1)). If the effective dwell time was counted from the time the center concentration reaches the predetermined value, then approximately 30 minutes would be saved in the latter case. Furthermore, the makeups with nitrogen (shown in green) during dwell may enhance the uniformity of the concentration distribution and alleviate the problem of poststerilization residues, as explained below.

The Sorption and Desorption Process

As shown in Equation 2, a source of EtO is formed in the load (sorption) at a rate proportional to the concentration, C, in the gas phase and released to the gas phase (desorption) at a rate proportional to its own concentration, S. During both phases, while (ksC – kdS) > 0, sorption is the dominant factor. As a consequence, the chamber pressure keeps dropping, and the loss in chamber pressure gives a measure of S. Makeups with EtO or nitrogen can be used to compensate for the loss in chamber pressure. In a hypothetical situation, however, if the process of dwell and makeups were allowed to carry on for an infinite period of time, the chamber pressure would gradually cease to drop and, consequently, there would be no more makeups. 

Figure 4. Display window containing diagrams (a4)–(d4) for cycle 1.   (Click to enlarge).

In this case, sorption and desorption had reached equilibrium (i.e., (ksCinf – kdSinf) = 0). In practice, the C and S data can be extrapolated to produce Cinf and Sinf, and thus (kd/ks) = (Cinf/Sinf). Because the relationship between the loss of chamber pressure or makeups and time is exponential, kd or ks can be determined using the regression method.

From a knowledge of the dynamics-related coefficients D, ks, and kd, one can calculate the EtO concentration dynamic distribution within the chamber at any time throughout the remaining sterilization cycle phases from the moment of first gas injection. 

In Figure 2(a2), cycle pressure and real-time spectrometer data are displayed until the time the gas dwell ends. For ease of description, Figure 2(b2) only displays the EtO concentration distribution at the time the gas dwell phase ends, Figure 2(c2) shows the EtO sorption distribution, and Figure 2(d2) illustrates the EtO concentration distribution in percent by volume. The sorption at the center of the load gives an approximate measure of the integration of EtO exposure (i.e., the sterility). For comparison, Figure 7(a2 – d2) displays those of the modified cycle (cycle 2). 

Figure 5. Display window containing diagrams (a5)–(d5) for cycle 1.    (Click to enlarge).

By comparing the two cases, it can be shown that toward the end of the gas dwell, the two have approximately the same sorption at the center, (i.e., approximately the same sterility), as shown in Figures 2(c2) and 7(c2). But better concentration uniformity is found in the latter case (see Figures 2(b2) and 7(b2)), and less residue is produced (Figures 2(c2) and 7(c2)).

During the air-purge phase, while (ksC – kdS) < 0, desorption takes the lead as the dominant factor. Air (identified by dotted green) is injected into the headspace following the vacuum phase. This dilutes the EtO concentration in the headspace and generates a positive surface-to-center pressure gradient that forcefully pushes the EtO gas toward the center, as shown in Figure 3(a3 to d3). Evacuation (shown in cyan) follows, removing the gas from the chamber and from the headspace, and generating a negative surface-to-center pressure gradient that pulls the EtO gas away from the center. At the same time, the EtO molecules immobilized in the load material are released to their gas phase. As a consequence, the EtO sorption decreases and EtO concentration in percent by volume in gas phase increases. This is illustrated in Figure 4(a4 to d4).

This process of air injection and evacuation is repeated several times. The EtO distribution is such that the highest concentration is in the center of the load and the lowest is on the surface. If the surface EtO concentration (i.e., that in the headspace), is reduced to below the lower exposure limit (LEL) level (3% of EtO by volume), then it is considered safe to open the chamber door. However, this is a tricky situation, because the processes of diffusion and desorption are continuing, and the EtO concentration in the headspace may again rise above the LEL level. This is shown in Figure 5(a5–d5).


EtO sterilization dynamics is generally considered to be complicated when one attempts to calculate the gas/vapor concentrations in a loaded chamber using the ideal-gas law.11 Variations in load elements, such as in packaging and raw materials, may alter the process behavior. This can present uncertainties in the calculation. In the method described here, however, those uncertainties are measured and attributed to three coefficients, D, ks, and kd, irrespective of the load elements. 

Figure 6. Display window containing diagrams (a1)–(d1) for cycle 2.   (Click to enlarge).

As indicated above, the ideal-gas law applies to the gas phase (including the headspace and void spaces inside the load), and pressure is uniform in these spaces. It should be noted that the void spaces inside the load do not include those in sealed packages, where the pressure may be different from that of the headspace. These sealed packages are treated as individual objects in the load space. Their effect on the mathematical model is taken into account in the load density, hence the diffusion coefficient.

Density is assumed to be uniform in the load space so that the materials in the load space are isotropic. Because the gas concentration in the headspace is uniform, the gas diffusion direction is considered to be radial towards the center of the load. The load is viewed as approximating a sphere (single-pallet chamber) or a long cylinder (multipallet chamber). 

The mathematical model was initially developed to interpret the EtO measurement data by the microwave spectrometer.2,3 Yet its potential applications as a software tool far exceed its initial intended purpose. 

Figure 7. Display window containing diagrams (a2)–(d2) for cycle 2.   (Click to enlarge).

The method is expected to help process engineers to optimize a cycle design to achieve sterility and low residues and, thus, shorten release time.11,12 It may help quality assurance personnel and process operators to understand the cycle parameters and safety issues. It may also help reduce the total time required to validate a particular sterilization cycle. Perhaps the most important benefit is that it may enhance the science of EtO sterilization and help the process to finally come of age, so that parametric release becomes generally accepted.1,12,13


1.IP Matthews et al., “Parametric Release in EO sterilization,” Medical Devices Technology 9, no. 6 (1998): 22.
2.Z Zhu, IP Matthews, and C Wang, “Gas Dynamics of Ethylene Oxide during Sterilization,” Rev Sci Instrum 70 (1999): 3150.
3.Z Zhu, IP Matthews, and W Dickinson, “Specificity, Accuracy and Interpretation of Measurements of Ethylene Oxide Gas Concentrations during Sterilisation Using a Microwave Spectrometer,” Rev Sci Instrum 68 (1997): 2883.
4. Z Zhu, IP Matthews, and AH Samuel, “Quantitative Measurement of Analyte Gases in a Microwave Spectrometer Using a Dynamic Sampling Method,” Rev Sci Instrum 67 (1996): 2496.
5. Z Zhu, IP Matthews, and AH Samuel, “A Microwave Spectrometer with a Frequency Control System Employing a Frequency Scanning Window Locked to the Rotational Absorption Peak,” Rev Sci Instrum 66(1995): 4817.
6. Z Zhu, et al., “Measurement of Gas Concentrations by Means of the Power Saturation Technique in a Microwave Cavity Spectrometer,” IEEE Transactions on Instrumentation and Measurement 43, no. 1 (1994): 86.
7. Z Zhu et al, “Triple Modulation Technique Applicable to Microwave Spectrometers with Cavity Gas Cell,” IEE Proceedings-H 140, no. 2 (1993): 141.
8. Z Zhu et al, “Cavity Modulation Coupled with Asynchronous Source Modulation in a Microwave Cavity Spectrometer,” Trans Inst MC 15, no. 1 (1993): 32.
9. Z Zhu et al, “A Gas Monitoring System for Ethylene Oxide Steriliser with Constant Sample Flow Through a Microwave Cavity Spectrometer,” Journal of Medical Engineering and Technology 17, no. 4 (1993): 147.
10. Z Zhu et al, “Microwave Cavity Spectrometer for Process Monitoring of Ethylene Oxide Sterilisation,” Rev Sci Instrum 64 (1993): 103.
11.PJ Sordellini, “EtO Sterilization: Principles of Process Design,” Medical Device & Diagnostic Industry 20, no. 12 (1998): 47.
12.PJ Sordellini, FR Bonanni, and GA Fontana, “Optimizing EtO Sterilization,” Medical Device & Diagnostic Industry 23, no. 8 (2001): 19. 
13.PJ Sordellini, “Speeding EtO-Sterilized Products to Market with Parametric Release,” Medical Device & Diagnostic Industry 19, no. 2 (1997): 67. n

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