Let's do a question on a difficult topic, volume of distribution.
So let's look at this question here.
A 25-year-old takes compound C, levels were measured and found to be 300 ng/mL.
The volume of distribution is 100 L. How much of C was ingested?
And there you can see the potential choices.
Now how do you answer this question and more importantly,
why do we care about volume of distribution?
And most importantly, I suppose is what is volume of distribution?
Now, volume of distribution is the volume or the potential volume of blood
that a person would have if concentration were to remain constant
and none of the drug were to be bound in tissues.
So here's an example.
Drug A permeates tissues without binding to a protein in the blood,
so that little blue squiggly line that you see in the vascular compartment,
that's a protein in the blood.
Now you can see that 18 units of the drug have gone into the extravascular compartment,
so that's the tissues, that could be the brain or the liver or whatever,
and only 2 units have stayed in the blood.
If you look at the formula at the top of the slide there,
volume of distribution is the amount of drug in the body divided
by the concentration in the blood.
So in this particular case, there is 2 units in the blood, there's 20 units of drug in the body,
so the volume of distribution is going to be 10.
Now let's look at a different drug. Let's look at a drug that binds to a protein in blood.
This B, a drug, has bound to the protein, so the squiggly little blue lines,
and only 2 units have entered into the extravascular compartment, okay?
Now, the amount of concentration, the amount of drug in the body is still 20,
but the concentration in the blood is 18, that gives you 1.1 L, so the volume of distribution is 1.1 L.
Drug C binds to the fat in the peripheral tissues, so this is an example of a drug,
say, that crosses the blood brain barrier and binds to fat or gets absorbed into fat inside
say, the fat of the brain or the fat of the belly or whatever.
This drug now has 200 units in the body, 2 units in the blood,
so it has a volume of distribution of a 100 L, so when you injected that drug,
it says, if that person has a 100 L of blood, because that's the concentration that you've achieved.
Now what determines volume of distribution?
A couple of things. First of all, what is the size of the organ that the drug is being distributed to?
What is the blood flow of the organ? What is the solubility of the drug?
And how much of that drug binds in the blood such as protein?
Now remember that any binding of a drug in the blood will decrease the volume of distribution,
and any binding of the drug in the extravascular space such fat or protein or bone,
will increase the volume of distribution.
So going back to this question, we can now plug in the numbers.
So the volume of distribution is equal to the amount divided by the concentration,
or we need to move the concentration over because we just want the amount.
By doing that, by dividing both sides with the concentration, we have a formula,
the volume of distribution times the concentration equals the amount.
So that's a hundred times three hundred is the amount.
Now a hundred is actually in liters and the formula shows that 300 is 300 ng/mL.
Well, we want to convert it into milliliters so a 100 L is a 100,000 milliliters.
Now we know that the units cancel out, the milliliters cancels out,
so we can multiply 300 x 100,000 and the answer is 30 million ng or 30,000 mcg or 30 mg.
So the answer to our question is 30 mg.
Now let's move on to a different kind of a question.
So a sick women in the intensive care unit has a resistant sepsis.
It's a bacteria that is highly sensitive to vancomycin.
The volume of distribution of vancomycin is 0.71 L/kg. The patient weighs 73 kg.
So now you see that the volume of distribution is not just being referred to as liters
but it's being referred to as liters per kilo, which sometimes happens.
If you see that then you need to calculate the weight of the patient.
Sometimes the VD does not have per kilo gram numbers
and so you assume that the patient is a 75 kg male.
Now how much drug should we give to this person
in order to achieve a concentration of 20 mcg/mL?
So the volume of distribution is the amount over the concentration,
you plug in the numbers including the weight of the patient and you get 0.71 x 73.
Now you move the concentration over and you get the amount, here is the math.
The math comes out to roughly 1,036,600 mcg or 1.073 mg, rounding that to the nearest gram,
that's about a gram of the medication so we are going to give this a women a gram of vancomycin
in order to achieve the drug levels that we want.
Case number four: A 28-year-old woman has been diagnosed with a rare infection.
The antibiotic, let's just call it substance J,
needs to achieve a concentration of 0.85 ng/mL in order to be affective.
Now she weighs 45 kg. The VD of the drug is about a 100 L/k,
how much drug should we give in order to achieve the effect of concentration?
Once again, we'll just plug in the numbers so here we go.
There's the volume of distribution, kilogram times the weight of the patient in kilograms
equals the amount over the concentration.
We move the concentration, we fill in the numbers, we multiply it out and here we have 4500 x 0.85
which gives you 3,825,000 ng or 3825 mcg or 3.825 mL,
so we round that out and we get about 3.8 mg. So the drug that we need is 3.8 mg.
Okay, this is another question. It's a very typical question that you'll see on your USMLE,
but more importantly some of you are actually gonna end up in this situation yourself.
Now imagine you are in a country hospital
and you don't have access to the most advance of laboratory equipment.
So an 8-year-old boy accidently ingests a drug four hours ago.
The volume of distribution of this drug in children is 0.75 L/kg and he weighs 40 kg.
He ingested 6 pills each of which is 300 mg.
You don't have access to a lab, but you know that if the concentration of this drug
exceeds 50 milligram per liter you will have to send this patient in,
by ambulance or by helicopter, for dialysis. So the question is, do you need to do that?
Once again, the volume of distribution equals the amount over concentration in this case
its volume of distribution per kilo so you need the weight of the patient, okay?
You enter in the numbers, the concentration, now, because we are asking for the concentration,
you move the concentration over to the left of the equal sign
and you get 1800 mg over 0.75 x 40, that's 1800 mg/30L.
The concentration is now 60 mg/L so yes, you need to send this person for dialysis.
You've managed to come up with this answer
without actually having to do the lab test to test the concentration of blood.
This is why volume of distribution can be really important to know as a practicing physician.
Well done. Good luck on your exams, you're going to do really well. Show them what you know.