Thermal sterilization kinetics in bioprocessing: How does the lethality (Δ, often called the “del factor”) change as the final survivor count after treatment decreases, all else being equal?

Introduction / Context:
Thermal sterilization and pasteurization are quantified using death-kinetics metrics. One convenient measure of total microbial kill is the lethality or “del factor” Δ, which accumulates over the heating, holding, and cooling phases. Understanding how Δ relates to the surviving cell count is critical for setting time–temperature schedules that achieve target sterility assurance levels.

Given Data / Assumptions:

• First-order (log-linear) survivor kinetics with respect to lethal exposure.
• Constant reference temperature or equivalently normalized time at a chosen reference (e.g., F0 at 121°C for spores).
• Same initial load N0; only survivors N_f vary due to exposure differences.

Concept / Approach:
For log-linear inactivation, the relationship between lethality Δ and survivor numbers is monotonic. A useful form is Δ ∝ ln(N0/N_f) (natural logs) or Δ_10 ∝ log10(N0/N_f) (decimal reductions). Smaller N_f (fewer survivors) means a larger ratio N0/N_f, hence a larger Δ, i.e., more lethal effect delivered.

Step-by-Step Solution:
Start with survivor equation: N_f = N0 * exp(−k * t_equiv).Rearrange: ln(N0/N_f) = k * t_equiv ≡ Δ (when expressed at a reference temperature).Observe dependency: as N_f decreases, ln(N0/N_f) increases.Therefore, the del factor Δ increases when the final number of cells decreases.

Verification / Alternative check:
Decimal reduction language: a 1-log reduction (10×) raises Δ_10 by 1; going from 10^6 to 10^0 survivors is a 6-log reduction, clearly indicating greater lethality with lower N_f.

Why Other Options Are Wrong:
“Decreases” or “remains constant” contradict the monotonic relationship between Δ and N_f.

“Becomes zero” would only occur if there were no lethal exposure or N_f = N0.

Common Pitfalls:

• Mixing natural-log and base-10 log definitions; be consistent about Δ versus D- and z-values.
• Ignoring contributions from heating/cooling ramps, which also add to Δ.

Final Answer:
Increases