# MathBench>Microbiology

## Viable Plate Count, or...How to count to a million

Remember Frank? He's still sitting on the examining table with a coat over his head. In fact about 50% of people with meningitis will die when the bacterial levels in their blood stream reach 500 / mL.

The worried nurse hands you a vial of 10 mLs of Frank's blood. How can you decide whether the infection is at a lethal level?

What counting method will you use?

Unfortunately, a direct count or a photospec would require separating the meningicocci from the red blood cells. If we could do that, we could probably just cure poor Frank. So we're stuck with a viable plate count.

What dilution scheme will you use?

We need to get plate counts between 30 and 300, and we think that the concentration in his blood might be as high as 500 per mL, but it could be much lower. So, we should go ahead do the first plate without even diluting! After that we could do standard 1/10th dilutions.

How many dilutions do you need?

You definitely need at least 1 dilution, in case Frank is somewhere in the 300 or 400 per mL range. Without a dilution, that wouldn't be countable.

But really, a single 1/10th dilution would suffice. If Frank has >300 colonies in a 1/10th dilution, he has >3000 actual cells per mL, and that would be fatal. (Of course, he'd also be dead, but let's not be morbid).

However, you could keep going with a standard 5 dilutions and not waste much time or energy, plus it would allow you to make an accurate estimate regardless of his actual level of meningicocci in the blood.