And the easiest way to do that is by looking at a graph.

Now, pay attention to the axis of this graph

because on the Y axis, we're going to put what we really care about in this lecture and that is, the rate of drug metabolism.

and we're going to see how that depends on the plasma drug concentration.

So, before we go any further, I need to implant an idea in your head.

And this is kind of a big picture thing.

We remember that with drug metabolism, we are dealing with enzymes.

and these enzymes are obviously located in the liver.

Now, we have more enzymes typically than we need at any given moment.

And so, these enzymes are just sitting around and they are waiting to work and we need to just keep this idea in the back of our head

because it will help explain the differences between first order and zero order kinetics.

So, if you were going to remember only one thing about first order kinetics, I would want you to remember

the relationship between the plasma drug concentration and the rate of drug metabolism

and the idea here is as I increase the plasma drug concentration, we are putting more of these enzymes to work

and as a result, I increase the rate of drug metabolism.

And another way of saying the same thing is that the rate of metabolism is proportional to the drug concentration.

Now what we want to do is differentiate this from zero order kinetics.

So, with zero order kinetics, we are at max capacity or full capacity

And so, what that means is all of our enzymes are working and what they're working on is the substrate,

the drug concentration.

So, if all of our enzymes are working, if I increase the plasma drug concentration, there are no extra enzymes to put to work

and therefore, there will be no increase in the rate of drug metabolism.

And so, once we get to this point, what happens is that the rate of metabolism has now become independent of drug concentration.

So, let's start off by drawing first order elimination.

So remember, as a plasma concentration is going up, we expect the rate of drug metabolism to go up as well.

So, on the graph as I move to the right which is increasing the plasma drug concentration,

we expect the rate of drug metabolism to go up as well.

And that is what we see right here.

So this is happening first. This is happening at the lower plasma drug concentrations.

This is the first order kinetics.

or first order elimination.

And what you need to remember here is that as I'm increasing the amount of drug getting to the liver,

as I'm increasing the plasma drug concentration, I'm recruiting more enzymes

and as a result, the rate of drug metabolism is going up as well.

So what I'm writing here is that the in is proportional to the out.

The in being the drug getting to the liver. The out being the metabolized product.

Now, after this plasma drug concentration, after this point right here, we have now maxed out all of our enzymes.

And so, as the plasma drug concentration increases, as we move to the right on this graph.

We shouldn't see an increase in the rate of drug metabolism and that is what we see here.

So after this plasma drug concentration from here to there, we are at zero order kinetics or zero order elimination.

And so, now the amount of drug getting to the liver, the in is not proportional to the metabolized product leaving the liver.

And so this is problematic. We don't like to be in this zero order plasma drug concentration range as clinicians.

and the reason is the plasma drug concentration's going up but the rate of metabolism isn't going up with it.

So what that means is that the drug can build up in the body so it can build up

and if the drug builds up, that can lead to toxicity or toxic side effects.

And so, the third thing you should remember for zero order kinetics is the rate of drug metabolism is constant.

With zero order, as I'm increasing the drug concentration, I have plateaued in terms of the rate of drug metabolism.

We call this being at Vmax. I'm at max capacity.

So the third thing I want you to remember for first order kinetics is while the rate of drug metabolism is not constant,

there is a term that we use which is constant and that term is the half-life.

And so, the half-life is the time it takes to metabolize 50% of the drug.

So why is this occurring?

Well, remember, for first order kinetics, the in is proportional to the out.

So that means that we are metabolizing a constant proportion of drug per unit time.

So, constant proportion per unit time.

So, if I told you that the half-life was 1 hour, what I'm saying to you is that 50% of that drug is going to be metabolized every hour.

Here's why this is cool. It doesn't matter how much drug you have in your body.

If I have 100 mg of drug, if 1 hour goes by, I know that a constant proportion will be metabolized.

I'll have 50 mg left.

And if I have 50 mg of drug in my body, if another hour goes by, how much do I have left?

I'll have 25 mg left and again, the reason this is occurring is because the rate of drug metabolism is proportional to the plasma drug concentration.

So, what was the rate up here?

Well, I'm at a higher dosage so I expect a higher rate.

I lost 50 mg in an hour.

Here, I'm at a lower dosage, a lower concentration so I would expect a lower rate

and I lost 25 mg in an hour.

So while the rate may not be constant, the half-life is.

And in terms of the information you get per drug so when you're in the clinic, what you will see when you look up the drug monographs is you'll get information on the half-life

and not the actual rate of drug metabolism.

So you might be confused.

Why would they give us the half-life and not the rate of drug metabolism?

Well the answer to this question gets us to point 4 and that is with first order kinetics, this is happening most of the time.

It happens with most drugs at most dosages.

So, it makes sense. If this is where we are clinically most of the time, we want to give you that value that is going to be constant

so that you can approximate how long it's going to take for that drug to get out of your body.

Now, for zero order kinetics, this is not happening most of the time.

This is happening in unusual circumstances and only when you give way more drug than you are supposed to.

and when you give that much drug, you saturate the enzymes and thus, your rate of metabolism becomes constant.

You're at Vmax.

Now there are 3 examples you should know that saturates the enzymes quickly.

There are 3 examples of drugs.

And those 3 examples are aspirin, phenytoin and alcohol. These reach zero order kinetics quickly in relation to other drugs.

Now, you've probably heard of aspirin and alcohol before but if you haven't heard of phenytoin, that's all right.

This is an anti-seizure medication and this just illustrates the point even more.

If you're giving a drug like an anti-seizure medication, you're typically giving it daily and if a person's taking a drug daily,

when you slightly increase the dosage right you're going to have a repeated effect and the drug can then build up in the person's plasma.

So what we need to be able to do is differentiate first order from zero order kinetics with words like we did here

but we also have to be able to do it looking at a plasma concentration vs. time graph.

So we're going to use a little table to keep tabs here and we're going to draw points on this graph.

So remember that with the rate of elimination, this is constant with zero order kinetics.

A constant amount of drug is being eliminated per time.

And so, the rate of elimination is the change in plasma concentration over the change in time.

So, pay attention to the units here.

The plasma concentration, the units are mg of drug per liter of plasma and the time we're going to use here is going to be hours.

So what we'll do is we're going to say the constant rate of elimination we see is going to be 2 mg of drug per liter of plasma per hour.

and let's just assume that we start at 8 mg/L.

So if I'm saying the rate of drug metabolism is 2 mg/L and this is per hour,

with zero order kinetics, the rate of elimination is constant so this is going to be the same all the way through.

So every hour, we lose 2 mg/L. So after 1 hour, I'd be at 6. After 2 hours, I'd be at 4. After 3 hours, I'd be at 2

and after 4 hours, I'd obviously be at 0.

So let's draw this on the graph up above.

I started at 8. After 1 hour, I'm down to 6. After another hour, I'm down to 4 and then I'm down to 2

and then after 4 hours, I'm very close to having all of this drug out of my body.

So I draw this graph and notice that I'm going to get a linear graph.

Now let's compare this to first order elimination which is happening most of the time.

So with first order elimination, a constant proportion of the drug is being eliminated per unit time.

And so the example we're going to use here is we're just going to say 50% of the drug is eliminated per hour

and I'm using the hour because it's simple and it allows us to compare these 2 graphs.

So using the same table, what I'm going to say is that every hour that goes by, half of that drug is being eliminated.

It's a constant proportion. So I started at 8 then I go down to 4. That's 50%. After another hour goes by, I go down to 2.

That's another 50% and then 50% of that is 1 and 50% of that is 0.5.

So if I look at the rate of elimination, remember for first order, we don't expect this to be constant.

It is going to be higher for the higher plasma drug concentrations.

So the change in plasma concentration, that's 8 mg/L minus 4 mg/L over 1 hour and so, that comes out to be 4.

And if I do that same calculation in each place, the next in the numerator, I'll have 2 over 1 and then I'll have 1 over 1

and then I'll have 0.5 over 1.

So the rate of elimination is also changing here.

Now, let's plot these.

I started at 8. After 1 hour, I should be around 4. After another hour, I should be around 2.

After another hour, I should be around 1 and then I'll be at 0.5 and if I did 1 more, I'll be at 0.25

There is no way this is going to be a linear graph so let's draw this.

What type of graph is this?

This is an exponential graph.

Now, I know you want to say that okay, so with first order, we always get an exponential graph but I need you to pay attention to 1 thing here.

Pay attention to the scale on the Y axis.

This is a linear scale and oftentimes, when we graph first order elimination,

we don't use a linear scale but we use a logarithmic scale.

And so, on the next slide we're going to look at half-life and we're going to look at logarithmic scales

and the reason we use logarithmic scales with first order elimination is because it helps us approximate the half-life.

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