The Math of Microbiology: Understanding Sieve Impact and Feller Correction in Air Sampling

 


In the pharmaceutica industry Environmental Monitoring (EM) is the heartbeat of contamination control. When we use active air samplers like the MAS-100, SAS, or EMTEK P100, we aren’t just pulling air through a plate; we are performing a precise physical and statistical operation.

For any EM professional, two questions are critical: How many holes are in my sampling head? and How do I account for coincidence error?

The Sieve Challenge: Holes and Accuracy

Active air samplers work on the principle of "impaction." Air is drawn through a perforated sieve head at a specific velocity, directing microorganisms onto an agar surface.

The number of holes (N) in that head determines the sampler's resolution. In our facility, we utilize three industry-standard devices, each with specific configurations:

MAS-100 (MBV): Typically features a 300-hole head. The MAS-100 is known for its high "impaction velocity," ensuring even the smallest viable particles are captured.

SAS (Super ISO): These heads are versatile but usually come in 219-hole or 487-hole configurations. The 487-hole version is often preferred for higher environments to reduce the chance of multiple particles hitting the same spot.

EMTEK P100: Generally utilizes a 300-hole pattern, designed to maintain a laminar-like flow through the head to protect the viability of the organisms captured.

The "Coincidence Error" Problem

Why does the number of holes matter? Imagine a sieve with 300 holes. If 300 microbes pass through, the laws of probability suggest that some holes will see two microbes, while other holes will see none.

On your agar plate, two microbes landing in the same spot will grow into a single Colony Forming Unit (CFU). Without correction, your final report would under-count the actual microbial risk. This is known as Coincidence Error.

The Solution: The Feller Correction Formula

To satisfy regulatory requirements (such as those found in USP <1116> or EU GMP Annex 1), we apply the Feller (Macher) Equation. This statistical formula calculates the "Most Probable Number" (Pr) of microbes that actually passed through the head.

The formula is expressed as:

Pr = N [1/N + 1/N-1+ 1/N-2+ 1/N-r+1]

Where:

N = Total number of holes in the sampling head.

r = The number of CFU actually counted on the plate.

Pr = The corrected, statistically probable count.

Practical Example

If you are using a 300-hole head (like on the MAS-100 or P100) and you count 50 CFU on your plate:

The Feller correction would adjust your final result to approximately 54 CFU. While a difference of 4 might seem small, in a controlled Grade C environment, that adjustment could be the difference between staying "In-Limit" and a mandatory OOL (Out of Limit) investigation.

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