How is the zone of inhibition formed in disk diffusion?

Question

Question

How is the zone of inhibition formed in disk diffusion?

What I mean by the formation of the zone of inhibition is not the ultimate visibility of such zone but the circumstances that result in the matter becoming settled and further incubation being merely done to reveal the endpoint of the experiment:

In general, the entire process is completed and the position of the zone of inhibition determined within the first few hours of incubation.
Barry AL. Procedure for testing antibiotics in agar media: theoretical considerations. In: Lorian V, ed. Antibiotics in laboratory medicine. Baltimore: Williams & Wilkins, 1980:1–23.

Prior research

The zone of inhibition is formed when a critical concentration of drug (that amount that is just capable of inhibiting microbial growth under the test conditions) reaches, for the first time, a density of cells too large for it to inhibit. The size of the zone of inhibited growth is determined by the distance that the critical inhibitory concentration can diffuse into the agar medium before a particular density of cells is reached. Thus, the diffusion test is actually a race between the drug diffusing from the reservoir and the microorganisms initiating growth.
Barry AL. Procedure for testing antibiotics in agar media: theoretical considerations. In: Lorian V, ed. Antibiotics in laboratory medicine. Baltimore: Williams & Wilkins, 1980:1–23.

I can't get to understand what's a/the critical concentration.

How I understand the matter:

The zone of inhibition is formed when a concentration of drug reaches, for the first time, a density of cells too large for it to inhibit, and any additional drug concentration reinforcement arriving from the reservoir won't make a difference.

if my understanding is right, how does it go with the prior explanation?

Answer 1

Despite its simplicity, the disk diffusion test is based on sophisticated physicochemical principles governing the dynamics of diffusion of antibiotics simultaneous to bacterial growth in an agar system.

Wanger, A., Disk diffusion test and gradient methodologies. Antimicrobial Susceptibility Testing Protocols, 2007

Inhibition

The process of keeping the cell mass in a given area constant.

Critical concentration

A critical concentration is the antimicrobial concentration required to inhibit a certain cell mass in a given area decisively so that it's irrespective of any future decrease in this concentration due to diffusion of the drug further from this area.

It seems to me that's why rapid AST (results being read immediately after the appearance of visible growth) can't be performed in some cases: the inhibition zone becomes smaller with further incubation as the drug concentration becomes less than the critical concentration for the current cell mass at the edge of the inhibition zone:

Occasionally there is another faint inner ring of delayed growth that represents viable cells initially inhibited by the concentration of drug at that point. As incubation continues, inhibited cells will eventually grow when the concentration of drug is reduced either by continued diffusion outward or by deterioration of the drug at incubator temperatures. An inner ring of delayed growth is most commonly seen with drugs which are primarily bacteriostatic. As incubation continues the inner ring of delayed or partial growth becomes increasingly visible and thus it would appear that the zone of inhibition becomes smaller as the incubation time continues. It is for this reason that the period of incubation must be standardized and held constant.
Barry AL. Procedure for testing antibiotics in agar media: theoretical considerations. In: Lorian V, ed. Antibiotics in laboratory medicine. Baltimore: Williams & Wilkins, 1980:1–23.

Critical mass

A critical mass is the cell mass required to counter a certain antimicrobial concentration in a given area decisively so that it's irrespective of any future increase in this concentration due to the diffusion of more drug concentration to this area.

The Critical concentration

It's a critical concentration for the cell mass found at the outermost point inside of what's going to be the zone of inhibition at a certain time called the critical time.

The Critical mass

It's a critical mass for the antibiotic concentration in the point just outside what's going to be the zone of inhibition at a certain time called the critical time.

Formation of the zone of inhibition at the critical time

A zone of inhibition is formed when a critical concentration of drug [the critical concentration] (that amount that is just capable of inhibiting microbial growth under the test conditions) reaches, for the first time, a density of cells [the critical mass] too large for it to inhibit.
Barry AL. Procedure for testing antibiotics in agar media: theoretical considerations. In: Lorian V, ed. Antibiotics in laboratory medicine. Baltimore: Williams & Wilkins, 1980:1–23.

The position of the zone of inhibition is determined at a point of time [the critical time] when the critical concentration of drug reaches, for the first time, a density of growing cells too large for it to inhibit. When the antimicrobic is added at the time incubation is started, the position of the zone of inhibition is determined after a critical time.
Barry AL. Procedure for testing antibiotics in agar media: theoretical considerations. In: Lorian V, ed. Antibiotics in laboratory medicine. Baltimore: Williams & Wilkins, 1980:1–23.

MIC vs Critical concentration

In broth microdilution, the MIC has access to all the cell mass equally and immediately, unlike in disk diffusion, where critical concentration reaches its coressponding mass gradually as time passes. This causes the fact that any cell mass will be subject to a subinhibitory concentration of the antibiotic before the inhibitory critical concentration. I think this needs to be considered when trying to relate the two factors.
To add, critical concentration is a concentration gradient not a concentration per se like MIC: as for the aforementioned reinforcements and outward diffusion.

Answer 2

Generally antibiotics don't actually kill the bacteria, all they do is inhibit growth so that you don't get any new cells formed.

Thus, if you have a drug diffusing away from the disk, at some point the drug will reach a concentration that allows growth of standard concentration (often 0.5 McFarland) of the bacteria applied to the plate. Even if the zone of high concentration extends out further from the disk due to diffusion, these bacteria will still be there (remember inhibited, not killed), so you will see these bacteria and have determined the zone of inhibition.

Now, you might be thinking this should result in a halo where you don't get much growth but still get some before the drug reaches inhibitory concentration. In practice, you do see this, but it tends to be minimal for the reasons below:

The concentration at any given point is dependent on the square of the radius of the zone (area = pi*r². To reach a higher concentration you need a lot more drug to shift the point. For a made up example - if you have a zone of inhibition with a diameter of 2 cm (i.e radius of 1 cm). To get this same point out a further centimetre, you would have a radius of 2 = 2² = 4x as much drug at each point around the circle. (I'm aware there's some problem with this math, it's just an illustration of the problem).

Diffusion rates in agar are also slow; in the order of 1-10 micrometres per second IIRC. This works out to be somewhere in the range of 100-1000 seconds (1.67 min to 16.67 min) per millimetre, which, in combination with the need for much more drug per increase in radius, results in the sharp zone of inhibition seen.