A Dairy Discrepancy: The Limits of Detection

“Holmes, it’s me, Cecilia. Our nitrogen analysis is wildly inconsistent; auditors are threatening a recall! I haven’t spoken to Baron Von Butterly yet, but when I do…” 
Her voice trailed off while Holmes did his best to assure her, “Stay calm, Cecilia, we’ll get to the bottom of this.”

In the detectives’ office, Miss Mapple is squinting at a crossword puzzle: “11 down, ten letters: Professional advice? Simply consult an ant! Hmm.” 
Noticing Holmes’s troubled look, Eggcule Poirot asks, “What’s wrong?” 
“My school friend Cecilia’s lab is in crisis due to flawed nitrogen measurements,” explains Holmes.
“Do you think it’s an issue with their Kjeldahl process or methodology?” says Miss Mapple. 
“I doubt it; Cecilia knows the process as well as I do; you lot help Miss Mapple with her crossword, and I’ll head to the dairy labs,” says Holmes before rushing out the door.

Tension filled the lab as Cecilia confided that the fearsome Baron Von Butterly could arrive any minute. According to the gossip, the untrustworthy Baron had asked his assistant to have a detective follow his wife, but the plan backfired when she disappeared with the detective. The Baron has been desperate to confront the detective ever since. 
“Well, I can assure you it wasn’t one of the food detectives,” says Holmes.
“Oh, I never thought so for a second, but the Baron… he’s not the most understanding, and if he arrives to find you poking around with your magnifying glass, who knows what might happen,” explains Cecilia.
“Then I shall waste no time, and with a bit of luck, I’ll be done before the Baron arrives,” says Holmes.

What can cause inconsistencies even if your process is perfect?

Shallot investigates every step of their process – sample preparation, digestion, alkalization, distillation, and titration - all done perfectly. They even implemented many of the detective’s top tips in their process. Shallot asks to see the audit report. 

“Hmm, the data for lower-level nitrogen products is unreliable, but for higher nitrogen levels, the deviation is less. I suspect that no single factor, but an interplay of multiple factors is to blame, such as an excess of dead volume in the glass apparatus that inflates your limit of detection (LOD) and limit of quantification (LOQ),” he explained. 

To fix the problem, Holmes demonstrates how upgrading to a new distillation unit—with auto-distillation mode and superior glassware—could reduce the LOD to 0.007 mg N and the LOQ to 0.02 mg N, but as he begins to explain LOD and LOQ, the lab assistants freeze in a state of horror. Holmes notices they are not looking at him but over his shoulder.

As Holmes slowly turns around, the full force of the Baron’s presence hits him. He freezes on the spot. It looks as if steam is about to burst out of his ears. 

“Who are you? Is that a magnifying glass? Are you a detecti..,” screams the Baron.

Thinking quickly on his feet, Holmes interjects, “Pleasure to meet you, Baron; I’m Dr… … Quantificus Titrant, a leading expert in analytical chemistry, specializing in detection limits and quantification.”

“Hmm, and I suppose the humble magnifying glass, is that what leading experts in analytical chemistry use these days is it… I always associated magnifying glasses with detecti..,”

Before the Baron can finish his sentence, Holmes blurts out, “Ah, this magnifying glass, this was, this is, umm, this is merely for a demonstration I was about to give to your laboratory staff to explain the issues you’ve been having.”

The Baron, teeming with suspicion, asks Holmes to continue his demonstration. 

What is an instrument’s limit of detection and limit of quantification?

Holmes turns to face the lab technicians, takes a deep breath, and says, “You all wash your hands before performing your lab duties, don’t you,” 

“Yes,” the lab workers say in unison.

“And why do you wash your hands?” asks Holmes.

“Bacteria,” responds one of the lab workers.

“Well, I can’t see any bacteria on my hands, so I suppose there’s no need to wash them,” says Holmes.

“The bacteria are still there, even though you can’t see them,” says Cecilia.

“Exactly,” says Holmes as he walks to the lab bench and holds up a sample. 

“And this is the issue you had with your audit. Using your current equipment, you searched for nitrogen in your samples, and for some of your samples, you could not detect any and thus proclaimed that no nitrogen was present. But, when the auditors looked at your sample, they looked a little closer,” says Holmes as he dramatically grabs his magnifying glass and holds it up to the sample. 

“And, because they could see closer, they could detect the trace amounts of nitrogen you missed, thus revealing the discrepancy. The problem you have in your lab is the limit of detection and limit of quantification,” says Holmes.

“I get it; the magnifying glass improves the limit of detection, but what about the limit of quantification?” asks the Baron.

“The limit of detection and limit of quantification refers to the minimum signal or quantity that can be reliably observed from a given signal with satisfactory confidence or statistical significance,” Holmes says before noticing a look of panic on Cecilia’s face as she notices that the Baron is getting confused and frustrated again.

“Umm, what I mean to say is…” 

As Holmes begins to panic, he spots a tiny ant crawling across his magnifying glass and wishes he, too, could be small and undetectable to get out of the situation. ‘Come on, little ant, help me out; how can I explain quantification to this big oaf?’ 

“The limit of quantification is more than being able to see the bacteria, or nitrogen in your case; it’s about accurately measuring the amount. Imagine a small ant crawling across some weighing scales that only measured in kilograms; it is unlikely that the scales would pick up the ant at all, even if you could see it,” says Holmes

“Haha. I get it, and if I stood on the scales, the needle would probably pop off the scale, and my weight would be undetectable too, ha ha ha ha haa,” said the Baron in a fit amusement. “hee hee hee, I like you, what did you say your name was again?”

“Shallo… … umm, I err, shall-o, Shall I remind you? Yes, yes.. umm Dr…”

“Quantificus Titrant” says Cecilia. “

“Ah yes, Dr. Quantificus Titrant, odd name, odd fellow, but who am I to talk ey, and you reckon this new equipment will help my lab see clearer and measure more accurately?”

“We ran a pilot test to verify the improved LOD and LOQ, then reran the nitrogen analysis the auditors questioned. The new system provided consistent data for low nitrogen levels—the results were repeatable, with minimal deviations. Moreover, the AutoDist mode allowed lab technicians to perform other tasks while the equipment ran, cutting down on idle time. I no longer need to babysit the machine,” explains Cecilia.

“We’ll see about that,” says the Baron as he grabs the latest samples and sends them for verification from the auditors. When the results confirm what Cecelia and Holmes said, the Baron is happier again. 

“Thank you, Dr. Titrant; if ever I need a consultant, I shall contact you and pay you handsomely for your time,” says Baron von Butterly.

Holmes leaves a contact number for Dr. Titrant and returns to the detective’s office. 

“Hello, detectives, how are you getting on?” says Holmes.

“We’ve almost finished the crossword; we are just stuck on one cryptic question,” says Nancy Beef. “Professional advice? Simply consult an ant!”

Holmes chuckles to himself. “It seems you all have a problem with your limits of detection. The answer is written right in front of you, but you can’t see it.”

The phone rings, and Cornlumbo answers, “Hello, can I help… Sorry, who… Dr. Quantificus Titrant… I’m sorry, you must have the wrong number; there are no consultants here. We’re all detectives,” says Cornlumbo before hanging up.

“No, Cornlumbo, Wait!” shouts Holmes.

“Ah yes, of course, consult an ant, CONSULTANT!” says Miss Mapple joyfully as she finishes the crossword.