Okay, let’s do a question. Let’s take a look at this particular case study.
This is going to be a correction for renal disease.
Now William is 68 year old. He has mild renal impairment and he has an infection.
He’s prescribed a drug, we’ll make it up, we’ll call it supercillin, there’s no such drug.
The following are the pharmacokinetic parameters of the patient.
Now remember that this drug is fully bioavailable just to make this equation a little bit simple.
At 100% renal excretion, this patient has a clearance of 1.8 L/hour.
The half time of this drug is 27 hours, the volume of distribution is 51 liters.
The EC minimum that’s the effective concentration, the lowest effective concentration is 25 mg/l
and the maximum effective concentration or what we call the toxic level is 63 mg/L.
Now what would be the appropriate loading dose for this patient?
Okay, how do we solve this equation?
Let’s start out with our loading dose equation.
Loading dose equation is going to take the volume of distribution times
the target concentration divided by the bioavailability.
Now, I’ve already said that it’s fully bioavailable so we don’t have to worry about that.
What do we mean by peak and trough levels and what do we mean by a loading dose?
So let’s talk about something called the therapeutic concentration that you can see here on my graph.
The therapeutic maximum concentration for theophylline is 16 mg/L,
the minimum effective concentration for this drug is 8 mg/L.
If we target 8 we’re targeting the trough level, if we’re targeting 16 we’re targeting the peak level.
The difference between the trough and peak is called the therapeutic window.
If we target that peak window remember that that peak value is actually a potentially toxic dose above
that so we don’t always wanna have the drug hovering at around that peak level.
What we try to do is we try to determine a peak and trough level of a drug
that lie between the minimum and the maximum effective concentrations.
When we give a loading dose, what we’re talking about is the first drug
that will get you to the maximum effective concentration or the minimum toxic concentration.
So the loading dose is this formula -
volume of distribution times the desired plasma concentration divided by the bioavailability.
So now let’s look at our therapeutic concentration of theophylline.
The therapeutic concentration window is between 8 and 16,
so what if we wanna get right down the middle of that dosing regimen?
So what we want for the optimum dose, not the maximum and not the minimum,
not the peak or trough but the optimum dose - we wanna get on that purple line.
The way that we calculate that is we take the maximum concentration,
the minimum concentration; we get the difference between the two, we divide it in half
and then we add that to the minimum concentration. So in other words we have 16 minus 8
divided 2 plus 8 so that’s 4 plus 8 equals 12, so the target concentration that we have here,
that we want in this patient is 12.
Now the therapeutic concentration window for theophylline as I’ve said before is between 8 and 16.
Slope of the drug curve is called the elimination rate so as that drug is getting eliminated from the body,
you know that it’s somehow either being excreted by the kidneys
or being broken down by the liver or another mechanism.
Generally speaking, for most drugs,
the elimination rate is synonymous with the renal elimination rate and most of the time
when you’re doing a question and they don’t tell you how it’s eliminated,
just assume that it’s renal unless they say it otherwise.
Now, if we know the elimination rate, if we know the peak concentration rate,
we can calculate when the patient will reach the minimum inhibitory concentration
from the maximum or the optimal dose so this will determine our dosing interval.
If we achieve the maximum concentration with our loading dose,
we know when it’s going to be the minimum dose and that’s gonna be our dosing interval
so in this particular case you can see that this person requires another dose every roughly 8 hours.
The dosing interval is calculated this way - the plasma concentration peak,
minus the plasma concentration trough divided by the elimination rate or the clearance.
Okay, let’s go back to William. What would be the required loading dose for this patient?
The loading dose is the volume of distribution times the peak concentration divided by bioavailability -
I already told you that this is a 100% bioavailable so dividing by a 100% is like dividing by 1
so we just get rid of bioavailability out of the equation.
We now have 51 liters times 63 mg/L equals 3213 mg or roughly 3 grams.
What would the dosing interval be? Well, we already know the creatinine,
we already know the clearance of this drug, so the dosing interval
is gonna be peak minus trough concentration divided by clearance,
so we have 63 minus 25 divided by 1.8 - remember, the units have to match
so make sure you do any conversion of the units aren’t matching -
you get 38 mg/L divide by 1.8 mg/hour and you get 21 hours as your answer.
So the dosing interval is gonna be roughly 21 hours.
Now the question here is what would the maintenance dose be?
Maintenance dose is a new term.
What we mean by maintenance dose is how much you are going to give at each dosing interval after your loading dose.
Remember your loading dose can be different from the maintenance dose.
We calculate the maintenance dose with this equation - serum concentration times the clearance of the drug.
When we plug in the numbers this is how we come up with the answer.
You can see here that I've substituted all of the numbers into the equation,
we shortened it up so that we make it a little bit easier to see
and we end with an answer of 1900.8 mg/day, that’s your maintenance dose.
The renal clearance as we come back to the slide is the original dose multiplied
by the creatinine clearance divided by a 100 mL/min so this is how we define renal clearance.
So when we have a calculation here and we’re saying his creatinine clearance is 66 mL/min,
what would be the maintenance dose?
We say, alright, the original dose multiplied by the creatinine clearance of the patient
so that’s the kidney function of the patient not the clearance of the drug itself divided by a 100 mL/min,
you get 1.6 g/day times 66 over 100 and what you have here is 1056 mg or about a gram a day.
Now why do we divide it by a hundred mL/min?
That’s because the creatinine, the perfect creatinine clearance of a patient is going to be estimated at a hundred.
That’s not always a 100% accurate but just for the sake of calculating, that’s how we do it.
So if you’re creatinine clearance is 66 mL/min, what we’re essentially saying
is that you have about 66% renal function or renal clearance so that’s why we divide it by a hundred,
it isn’t because it’s something that’s built into a formula otherwise it’s just a percentage
and we’re converting the number into a percentage.
One can change the interval of the dose to account for changes in the renal function
so if the renal function suddenly drops, let’s say the patient develops interstitial nephritis
and the kidney function plummets we have to be able to change on the fly our dosing intervals
and regimens based on kidney function.
Why do we learn all of these stuffs? Why am I teaching you these stuffs?
That’s because, first of all, it’s gonna be on your exams but secondly,
when you're practicing out in the community or whereever it is that you end up,
you have to recognize that a patient’s kidney function can change day to day, literally day to day,
so you have to be able to know how to make changes to your dosing regimens
based on the patients kidney function.
We can change the interval or the dosages based on patient kidney function
and make the drug safer for the patient so we’ll be able to achieve therapeutic concentrations
we need regardless of kidney function.
Okay, that’s it for this particular sub-lecture. Go write your exams, you’ll do well. Show them what you know.