This chapter considers the changes in the number of survivors (individual microorganisms capable of reproduction) with time. It is often applied to industrial disinfection, pasteurization, and sterilization (terminal or commercial sterilization) processes aimed at assuring safety, stability, and quality of pharmaceutical parenteral drugs and devices and of shelf-stable food products. These concepts can be studied using a variety of individual microorganism types or even mixed populations. But the emphasis of this chapter is focused on the inactivation of bacterial spores because they are highly resistant to antimicrobial agents and also have stability properties that support their use as biological indicators to verify the efficacy of sterilization processes (see chapter 65). Development, improvement, and troubleshooting of sterilization processes benefit from a good understanding of related inactivation kinetics.¹,² When a validated mathematical model is available, the related tasks may be supported more efficiently than using a purely empirical trial-and-error approach because the time, money, and other resources are significantly reduced. Indeed, in the food industry, a simulation package is well accepted by the regulatory and process authorities for simulation of moist heat-based (F₀; see equation 10 and chapters 11 and 28) processes.

Bacterial spore structure, formation, and significant transformations are well understood³ (see chapter 3). The significant transformations concerning sterilization are dormancy, activation, inactivation, clumping,⁴ and injury. Figure 7.1 presents a system diagram that includes these transformations and the corresponding subpopulations. “D” is applied to the inactivation transformation of the different subpopulations, and the inverted triangles represent the inactivated individuals corresponding to the different subpopulations. System analysis from population dynamics is used here to work on the corresponding models at the conceptual and mathematical levels. Dormancy is the transformation of the bacteria into its corresponding spore that renders it resistant to antimicrobial processes (see chapter 3), including moist heat, and microscopically birefringent. Activation is the transformation of dormant bacterial spores that enables them to potentially germinate into an actively dividing cell that can produce colony-forming units (CFUs) on culturing. Activated spores lose their high heat resistance and birefringence (looking opaque in the phase contrast microscope, discussed in the following text). Inactivation is a transformation of microorganisms that renders them unable to multiply and therefore produce CFUs. Clumping of bacterial spores (and other microorganisms) is where they form groups or clumps, but due to this affinity may only produce one CFU per clump of cells on cultivation. Finally, injury renders them initially incapable of producing a CFU, unless modified growth conditions (such as additional nutrients, lower incubation temperature, enzymatic treatments, extended incubation time, etc) are applied or occur. Other transformations have been conceptually described⁵ but have not yet been described mathematically well enough for practical applications.

Survival curves, which are generally semilog plots of the ratio of the concentration of surviving organisms to the initial number versus time, are commonly used to present inactivation data and to interpret the inactivation kinetics of microorganisms. Typical curves may be linear but are frequently observed to be nonlinear. Figure 7.2 presents some microbial inactivation curve types that may be seen in practice due to the presence of the different subpopulations and transformations described earlier. For instance, activated spores or vegetative cells will lead to an initial sharp drop in survivors because activated spores have a significantly lower resistance to moist heat that is similar to the resistance of vegetative cells. In addition, the activation transformation leads to a negative exponential curve and will lead to a hump
in the inactivation curve that may be significant at relatively lower temperatures and other conditions. These survivorship/inactivation curves may be described by the validated models available. Despite this, it is important to design products and processes that minimize the complexity of the description of the kinetics of inactivation without introducing significant error in practical terms. For instance, a more resistant subpopulation that may occur at occluded interfaces between glass and rubber stoppers may be eliminated by supersaturating the stoppers with water before sterilization, for example (see chapter 28). Figure 7.3 gives examples of how dormant bacterial spores change when viewed under phase-contrast microscopy. Dormant spores show birefringence and are heat resistant, whereas bacterial spores that have broken dormancy look opaque and have lost their high heat resistance. The bacterial spore resistance properties were recently reviewed.⁶

Conceptually, the inactivation of microorganisms under the effect of a lethal agent follows well-defined patterns, with the rate of inactivation diminishing with time in a mostly ordered fashion. The exponential nature of inactivation prevents the goal of zero survivorship from being realistic (infinite time would be required). Thus, low levels of survivorship have been defined and validated practically as the goals of related industrial sterilization or disinfection (including pasteurization) processes, such as terminal sterilization for the medical device and pharmaceutical industry and commercial sterilization for the low acid-canned foods in the food industry. This chapter reviews procedures that can be used to assist in the efficient development and validation of such processes. The complexity and diversity of industrial sterilization processes precludes the selection of a single approach to describe mathematically the inactivation of microorganisms. In addition, different lethal agents may attack different components of the targeted microorganisms (see chapter 5). For instance, DNA, enzymes, or other subsystems required for germination and growth may be targeted and can affect the results. Finally, study of the kinetics of microbial inactivation caused by some lethal agents such as radiation may benefit from a non-homogeneous kinetic approach (see chapter 29). As an illustration, Figure 7.4 presents the damage caused by an electric field in a piece of wood. Clearly, if electroporation was intended as the lethal process, some regions would receive high-intensity treatments, whereas most of the material would receive negligible treatments. Therefore, the model used to describe the corresponding kinetics of inactivation should be the simplest model that describes the inactivation process properly. Models with corresponding degrees of complexity are further discussed in this chapter. Moist heat (including ultrahigh pressure), dry heat, chemical, and radiation sterilization processes are reviewed in detail, due to their practical importance. Application of mathematical models to such practical problems is currently enabled using mathematical software in various computer systems. Use of mathematical programs eliminates the need to use traditional procedures (eg, semilog paper). Examples presented here as illustrations correspond to worksheets developed using MathCAD versions 14 or 15 (MathSoft Engineering and Education Inc, Cambridge, MA). The worksheets presented have been carefully developed, but no warranty is given regarding their application. Computerized systems must be validated properly in each instance per the corresponding regulatory requirements or guidelines.