Here is a case study, compound C. A 25 year old takes
compound C. Levels were measured and found to be 300ng/ml.
The volume of distribution is 100L. How much C was ingested?
Okay so this is an interesting question because we start to
introduce concepts of volume of distribution. The answers here
are clearly somehow calculated and give you an answer with
a 3 in it. The qestion is, what is the answer. Okay, what's
the volume of distribution. The volume of distribution is
the amount of drug in the body divided by the concentration
in the blood. Now that sounds kind of complicated
but let me explain it to you with some pictures. So let's
take a look at drug A. We put drug A into the blood
and after it diffuses across various membranes, you have
2 units of drug A in the blood or the vascular compartment.
And you have 18 units of drug A in the extravascular
compartments. Let's say it's in the tissues or in the
interstitial tissues. Okay, what's the volume of distribution
here? Well there is 2 units in the blood and there is 20 units
overall. So the volume of distribution is 20 divided by 2 or
10. It's in litres so it's 10L. So, when you think about it
it's as if you have 10L of blood. You and I both know that
we each have 6L or 7L of blood in our body. But it's as if
with the way that the drug is moving that we have 10L of blood.
Okay, let's take a look at drug B. This is a different kind
of a drug because now it's being bound to a blood protein.
You can see that it's all almost all in the blood compartment
bound to a protein. The fact that it's bound to a protein is
kind of irrelevant here. Only 2 units are in the extravascular
tissues. So what's the volume of distribution? Once again, it's
20 divided by 18 which is 1.1. So now, it's as if you only have
1.1L of blood. So the volume of distribution is 1.1L. What
about drug C? So now we have drug C. 2 units are in the blood
and 198 units are in the extravascular tissues. The volume
of distribution is 100 because it's 200 divided by 2.
So the higher the volume of distribution the more tissue
bounded is or the more it's in the tissues. Let's talk about
the determinants of distribution of a drug in the body.
It's going to be proportional to a number of things.
First it's going to be proportional to the size of the
organ. It's going to be proportional to blood flow.
It's going to be proportional to solubility and it's going to
be proportional to how much it binds. So it could be binding
to a protein, it could be binding to a cell membrane, it
could even be binding to bone. So it depends on each drug.
So we talked about compound C sometime ago. We talked about
this 25 year old who takes compound C, the levels were measured
and found to be 300ng/ml. The volume of distribution is 100L
and how much C was ingested? Now you know why this calculation
why this number is so important. So let's do the calculation.
So the volume of distribution is equivalent to the amount
divided by the concentration. So here we have, then we move
concentration over so we move it from the denominator into the
numerator. So the volume of distribution times the concentration
gives you the amount that was ingested. 100L times 300ng/ml.
Well you have to convert that to mL so it's 100000mL times
300 ng/mL. The mL cancel out. So you get 30000000ng or 30000ug
or 30mg. So when we go to our answer we can see that there is
a 30mg there and that's the one that we are going to choose.
So you can see that you are going to need to use math on your
USMLE exam when you are answering some of this questions.
Sorry about that. Let's try another question. Here is a sick
women in the intensive care unit. A women has a resistant
septic infection with a bacteria that is highly sensitive
to vancomycin. The volume of distribution of vancomycin is
0.7L/kg. The patient weight 73kg. How much drug should we
give in order to achieve a concentration of 20ug/mL. Okay.
So we've added something here. We have added volumme of
distribution per kilo. So remember in this case we have to
multiply it by the patient weight. Let's do that. We have
volume of distribution times the kg where the weight of the
patient equals the amount over the concentration. So we do
the same calculation and you can see on your own that you get
51.83L times 20. And our answer is going to be 1g.