Understanding Ke0

Once you understand this concept, it will hopefully make sense:

Why propofol works in thirty seconds but midazolam takes a while
When to choose alfentanil vs fentanyl

As always, we'll start simple and build from there.

You've just injected propofol

Hopefully into a vein, and as a result the plasma concentration of propofol skyrockets.

The extent to which this occurs of course depends on how much you give and how quickly, but either way - there's a lot more propofol in the plasma than there was before.

Then the plasma concentration starts to drop as two simultaneous processes occur:

Redistribution of propofol into brain, muscle, fat and other organs
Elimination of propofol from the blood by the liver, lung and kidneys

So the graph looks like this.

You can see the plasma concentration drops very rapidly at first and then more slowly over time.

This is because the concentration gradient between the plasma and the tissues is initially enormous, and then steadily declines as the drug redistributes.

Redistribution is responsible for the rapid initial drop in plasma concentration.

Eventually you're left with a very low plasma concentration that slowly gets whittled away by metabolism and elimination until there's none left.

Elimination is responsible for the much slower decline later on.

Simple enough so far.

Plasma concentration doesn't matter

This is quite clearly a lie - plasma concentration is enormously important - but what we mean by this inflammatory clickbait heading is that it's not the plasma concentration that determines the clinical effect of a drug.

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It is the effect site concentration that matters, and for most of our anaesthetic drugs, that effect site is in the brain.

This is why your patient takes a little while after you inject the propofol to actually fall asleep, because while their plasma concentration may be astronomical within seconds of administration, the effect site concentration lags behind.

So the graph looks like this.

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The peak effect of propofol occurs about 90 seconds after injection.

This lag happens because the propofol has to travel from:

Arm to heart
Heart to lung
Lung to heart
Heart to brain
Plasma to extracellular fluid
Extracellular fluid to neuron

And then find some GABA-A receptors to play with and knock the patient unconscious.

How quickly this happens depends on a multitude of factors.

What factors affect the speed of onset of propofol?

Dose and speed of injection - bigger concentration gradient
Cardiac output and cerebral blood flow - drug delivery to the brain
Ke0 - a composite of multiple factors - see below
Age - lower effect site concentration needed for unconsciousness
Other drugs - premeds reduce the required concentration for unconsciousness

So what's Ke0?

This is a rate constant.

Rate constants describe how easily and quickly a drug moves between body compartments.

If you've never seen this image before, I'd recommend heading over to this post quickly to come up to speed:

If you have seen this image before, then a quick reminder:

K01 is you putting the propofol into the vein
K12 is the propofol moving from the plasma to the highly vascular tissues
K13 is the propofol moving from plasma to fat and muscle
K31 is it moving back again
K10 is the elimination from the body

You get the idea.

Each time the drug diffuses into a different compartment, we can describe its willingness to do so using a rate constant.

Now the effect site is a mythical magical place that isn't actually a discrete physical compartment, it's a mathematical fudge to explain why it takes longer for propofol to show its clinical effects than it does for the V1 concentrations to change.

This is why it gets labeled Ke0.

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Ke0 is how fast a drug slips across from blood to effect site.

Every drug we give has a different degree of 'slipperiness' in how quickly it reaches the effect site, which dramatically changes how they behave.

Let's compare alfentanil and fentanyl

Finally, some actual clinical relevance.

Alfentanil has a Ke0 of 0.63 /min.

This means if you have a steady plasma concentration of 100 ng/ml, then the effect site concentration will initially* rise at 63 ng/ml/min.

Pretty damn slippery.

Fentanyl meanwhile has a Ke0 of 0.11 /min - which would mean an initial rise of 11 ng/ml/min in effect site concentration.

Less slippery.

This is why alfentanil has a time to peak effect of 1 - 2 minutes, while fentanyl takes a languishing 3 - 5 minutes to properly kick in.

Why does this matter clinically?

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Alfentanil can be used to react to a surgical stimulus, while fentanyl should be used several minutes before in anticipation of it.

*The initial is in bold because it's 0.63 of the concentration gradient, which is 100 to start with. As soon as some drug has diffused across, the gradient drops slightly, and so does the rate. For the purposes of our understanding, this is academic.