>> Welcome to the Dosage Calculation tutorial.
Please refer to your handout.
An antibiotic is prepared in a 3 mL ampule
that contains 60 milligrams of drug.
How many milliliters of the solution should be administered
to a patient prescribed 45 milligrams per injection?
All righty.
So the first thing we have to do is pull out the information.
Right here is the key: We're told that we have a 3 mL ampule
that contains this amount of drug.
So this is our conversion factor.
We know that we have 60 milligrams
of the drug per 3 milliliters.
So that's going to be our key to solving this problem.
Now, where to begin?
That can also be a challenge.
Well, what are we try -- how many milliliters,
that's what we're trying to calculate.
So we want a volume, all right, in milliliters.
All right.
And we're -- we know that the patient needs 45 milligrams
of drug, so we start here.
And really, once we've dissected the question,
it's really the only piece of information left
out so it's a natural starting point.
So we'll begin here.
The patient needs 45 milligrams of the drug,
and we know that there are 60 milligrams
for every 3 milliliters.
So we want to convert from the mass of the drug to the volume
of the solution to be administered.
And the conversion that's going to get us there is right here.
So if milligrams are on the top,
we want to make sure we have milligrams of drug
on the bottom, and we know that that's going to be 60.0,
and those 60 milligrams are contained in the 3 mL ampule.
So now we've canceled out the milligrams of drug
and we've been left with a volume.
So our setup is complete.
It's time to punch the values into the calculator
to get our final result, and we'll see
that the patient would need 2.25 milliliters.
And if we go, then, last but not least, we savor the moment
that we've solved the problem, and then we're back to sig figs.
So if we look at the sig figs, we have 45 would be 2,
2 here for the volume, and 3 here.
So we want to round our answer to 2 sig figs,
so 2.3 milliliters would be the correct volume
to inject in the patient.
All righty.
Let's try a few more of these.
There's many ways they can be asked,
and we'll get a little more practice before I set you off
on your own.
Ivermectin is a drug that is used to treat dogs
that have intestinal parasites.
The effective dose for this drug is, there needs to be
at least 1.5 micrograms per kilogram
of body weight for the animal.
So how much Ivermectin should be given to a 17-pound dog?
So right here, this is the key that's going
to get us to the answer.
All right.
So this statement right here tells us
that there's 1.5 micrograms --
and we'll just use an upper case I to represent Ivermectin,
right -- is equal to 1 kilogram of the body weight.
So that's the key piece that's going to connect us
from the body weight of the dog
to the correct dosage of the drug.
This one is a little more challenging
than the previous one because the weight
of the dog is in pounds.
So we have our 17-pound dog, but the link we have
to connect the body weight to the drug is in kilograms,
so we're going to need to do a unit conversion.
We'll need to go from pounds to kilograms, right.
And this is all has to do with the body weight of the dog.
And then once we have that conversion completed,
then we can bring in our dosage that for every kilogram
of bodyweight, we have 1.5 micrograms of Ivermectin.
So by now, you've probably got this memorized, right.
There are 2.205 pounds in a kilogram.
So the actual values here are important to do the calculation,
but it's important to note that the units are what guided us.
We were given pounds, and we're like, oh,
that's not going to help.
So we converted those pounds into kilograms.
Once we had the body weight in kilograms,
then we could apply the dosage,
and so then we could convert those kilograms of body weight
into micrograms of the drug.
So our units look right, and we'll go ahead and plug this
into our calculator and see what result we get.
All right.
And the calculator tells us 11.56 micrograms of Ivermectin.
And then last but not least, we take a moment
to savor the success and then look for those sig figs.
So looking at each piece of data, here we have 17 pounds,
2 sig figs; here this conversion gives us 4;
and the dosage gives us 2.
So we want to report our answer to 2 sig figs,
and when we look here, right, so that would be 12.
We're going to round up, so 12 micrograms of Ivermectin.
And it's important to remember too
that in the health community, they don't use the micro symbol.
They would write this as mc grams, micrograms.
So it's important to recognize the Greek "micro" or the mc
to represent micrograms.
Okay. So let's move on to a few more practice problems
because practice does make perfect.
Okay. There we go.
All righty.
So for this question, the doctor ordered 20 milligrams per
kilogram of medication for a patient that weighs 36 pounds,
and the medication is available 100 milligrams per milliliter.
How many milliliters should we give the patient?
All righty.
So this question has a couple different layers to it.
First, we have to figure out how many milligrams
of drug is needed for a patient weighing 36 pounds,
and then from there, we can know how much
of the solution to administer.
All right.
So let's -- let's dissect this here.
We have 20 milligrams of the drug, right,
for every kilogram of body weight.
And then we need some more information about the drug,
because the drug is not administered as a solid,
it's administered as a solution.
So we know that there are 100 milligrams of the drug
in every milliliter of the solution,
and so the solution is what's actually going
to be given to the patient.
It all starts with the body weight, right.
So we've talked about this conversion here
and this conversion here.
We're trying to find a volume.
So the only piece of information we haven't used
yet is the body weight of the patient
so that's where we'll start.
The patient weighs 36 pounds.
So just like our previous problem, we've got --
those pounds are not going to help us
with the information we've been given.
So we know there's 2.205 pounds
in every kilogram of body weight.
So now we will use the first piece of the information
and determine the amount of drug the patient needs.
For every kilogram of body weight,
the patient needs 20 milligrams of the drug.
So now we're out of the --
out of body weight and into the drug.
The drug is available to us in this solution;
and in this solution, there are 100 milligrams of drug
in every milliliter of this solution.
So now let's step back for a minute and check our units
and see if this calculation's making sense.
We started with pounds that we converted to kilograms
of body weight, and then we went --
converted from kilograms of body weight into the dose of drug
that we need, and then we used the concentration
of the drug solution to get the volume,
and so we're left with volume units.
So the units have indicated we've set this up correctly,
so we'll go ahead and plug it into our calculator,
and the result we get from the calculator is 3.265 milliliters,
right, of solution.
And so now we take a moment
to report the answer using correct sig figs,
and so this final answer should be reported to 2 sig figs,
and so the final result would be 3.3 milliliters of solution.
All righty.
Okay. Now, let's move on to the next question.
Slide this up so we have a little more room.
All righty.
A young child is being treated for a severe ear infection.
The pediatrician prescribes amoxicillin at a daily dose
of 40 milligrams per kilogram to be given
in three injections eight hours apart.
All right.
So this is a really powerful statement.
The thing to keep in mind here is, this is the daily dose,
but notice it's going to be divided
into three separate injections.
If the amoxicillin is supplied as a solution
that contains 125 milligrams of amoxicillin per 5 mL of liquid,
then how many milliliters should the child receive
in each injection?
The child weighs 7.64 kilograms.
All righty.
So the first thing we need to do is figure out the daily dose,
and then we're going to take that daily dose and we're going
to divide it into 3, and then we'll figure
out what the individual injection amount should be.
All righty.
So once again, we're going to start with the body weight
of the child, but let's see what other information we have here,
right.
So the daily dose is 40 milligrams per kilogram
of body weight.
Notice that starts to get left off;
we're supposed to know that.
All righty.
And then the amoxicillin solution is 125 milligrams
of amoxicillin equals 5 milliliters of solution.
All righty.
Okay. So I -- hopefully, you're starting to notice a pattern
that all of these dosage calculations start
with the weight of the patient, whether it's a dog or a child.
All righty.
So we have 7.64 kilograms, and we'll just do
"bw" for the body weight.
All righty.
And so there's 40 milligrams --
and this would be the amoxicillin --
per kilogram of body weight, all right,
and that's the entire dose.
So now we're going to --
we're going to divide that into thirds, right.
There's 3 injections per 1 day.
All right.
So those units aren't going to --
so this part, the units are a little funky,
but we'll sort it out at the end.
All righty.
So this was the body weight and the amoxicillin.
And so, then, what do we know about the amoxicillin?
We know there's 125 milligrams of amoxicillin in 5 milliliters.
So we have everything we need.
7.64.
Okay. So there would be --
it would be 4 milliliters per injection.
The calculator gave us 4.07 milliliters, and if we look
at our data, we have 1 sig fig in several places, so 1 sig fig.
So there we go.
There's a practice
with a slightly different type of question.
Another way -- so patients are administered drugs
through injections or serums or pills, but many times patients,
are given their medication through an IV solution.
So let's look at some IV calculations.
These are a little different
because we have the flow rate of the IV solution.
So that can be either the dosage per unit time,
or sometimes it's the volume of IV solution that is flowing
into the patient over time.
But remember that every time we see "per," right, you can think
of per as the equals sign, right.
So there's some sort of amount per unit time.
And so let's apply this now.
So for example, a medication is given intravenously at a rate
of 250 drops per minute.
All right.
So there's 250 drops of a solution, right, every minute.
So that's what this statement's telling us.
The medication's concentration is 450 nanograms per microliter.
And I've written it both ways to remind you
that the micro symbol can also be written as mc.
All right?
So now this gives us information about the solution.
Now we know a little more about the solution.
There's 450 nanograms of the drug
in every microliter of the solution.
So you see the bridge here.
We know the drop rate of the solution per minute,
and now we know the concentration
of the drug in the solution.
So then the question asks: What is the weight in grams
of the medication delivered to the patient in 24 hours?
And for this one, we have some extra piece of information
to connect drops to milliliters.
All right.
So this will be handy as well.
So we've used all the information
in the question except the time.
All right.
So we're trying to figure out the grams in a 24-hour period,
so this is where we start.
So I recognize that when we have a question like this
with so much data and information,
it can feel a little overwhelming,
so I really encourage you to just look at each sentence
by itself and think about what that sentence means,
and then when you're all done reading the question,
you have all the pieces of information,
and so then you can put them all together to tell the story.
So let's start with 24 hours
because that's what we're asking, right,
the grams in 24 hours in a day.
Okay. So hours are here, and we have minutes here.
So we've got a unit disconnect.
So what we know that for every hour, there are 60 minutes.
Now that we've converted into minutes, we can connect
into the IV solution through its drop rate.
So the question tells us, in each minute,
250 drops of solution will flow into the patient.
We have this little handy hint here, that there are 15 drops
of solution per 1 milliliter of solution.
And so the other thing that's going to be helpful
in solving these kind
of questions is the additional descriptors.
Like, it's not enough to say 250 drops, right.
It's drops of the IV solution,
and that helps guide us to the next step.
So we've converted the drops of the IV solution
into milliliters, and then that leads
to this other bit of information.
But, ah, we have another -- we have another challenge here.
This question is given to us in milliliters
but we have information in microliters, right.
So for every milliliter,
there are 1,000 thousand microliters, right.
That's another one of the unit conversions you want
to have off the top of your head.
Now I'm going to have to write tiny.
Okay, so now that we're in microliters,
we can look at the concentration of this IV solution.
For every one microliter, there's 450 nanograms.
And then we'll squeeze in here at the very end,
the question wants the answer in grams, right.
So there are 10 to the 9th nanograms in a gram.
So this one looks a little trickier, and it is,
but part of it is just that we have layered
in several unit conversions on top of everything else.
So let's go back and look at the unit
and make sure everything makes sense.
We started with 24 hours in the day; we converted the hours
into minutes; once we had minutes,
we could use the flow rate of the IV to get us
from time to the IV solution.
Now that we're into the IV solution,
we know that there's 15 drops of solution per mL.
So we could get out of drops,
which is a very strange volume unit,
into something we're more comfortable like milliliters.
But now that we have more information
about the IV solution, we can find out about the drug.
Unfortunately, or, you know, for better or for worse,
here's milliliters, here's microliters,
so we do another unit conversion, right.
So here's our -- let's see.
And this is another unit conversion.
Okay. And now we have the concentration
of the IV solution: 450 nanograms per microliter.
And then one last unit conversion.
So now we've got our hands full,
we've got a pretty lengthy calculation to do, so go ahead
and plug that into our calculator.
And it's important for you to plug these into your calculator
as well, especially when we have these exponential terms
because I want to make sure
that you're not getting any calculation errors,
because people die when there are calculation errors made
and we don't want that happening.
All right.
So then the calculator tells us
that that would be 10.8 grams in a day.
We'll go back, and as we check our sig figs,
let's make sure everybody's clear on sig figs here.
All right.
24 hours, so we'll say that's 2 sig figs; 60 minutes in an hour,
that's infinite sig figs because we have defined time.
It's really a made-up -- time is made up by us.
The flow rate is 2 sig figs.
This conversion here milliliters
to drops was given to us as 2 sig figs.
The metric system conversions, those are defined.
When they're defined, they have infinite sig figs.
All right.
And then last but not least, we have the concentration
of our IV solution which is also 2 sig figs.
So for our final result, we want to report it to 2 sig figs.
So the patient is going to receive 11 grams
of medicine in that 24 hours.
All righty.
Okay. Now we'll look
at a slightly different version of the IV solutions.
Here we have a patient that's given an intravenous morphine
at a rate of .35 milligrams per hour, right.
So this is telling us right here .35 milligrams
of morphine equals one hour.
Notice, right, it's a dosage per unit time.
At this rate, how many minutes will it take
to give the patient 1.5 milligrams of morphine.
So we're being asked to determine a time in minutes.
And where do we start?
Well, we're trying to find out, how long does it take
for the patient to receive 1.5 grams of morphine.
So this one's pretty straightforward
because we know the dosage per unit time of the IV.
So we'll just plug that in, .35 milligrams of morphine
in one hour, and so now we have the time, but, then,
it's always good to look back
and double check what units the question's asking
for the answer to be in.
Because if we stop here, we're not going to get full credit
because we haven't converted to minutes.
So then of course 1 hour is 60 minutes.
So we took the dosage of drug required
and then used the flow rate of the IV to get to time,
and then we used our definition of time to get the final answer.
So the units have indicated our setup is correct,
so we'll punch these values into our calculator,
and it will take 257 minutes for the patient to receive one
and a half milligrams of morphine.
And, then, for our coursework, we want to make sure to round
to the correct number of sig figs.
So 2 sig figs, 2 sig figs here, and then, of course,
infinite sig figs here.
You could say this exact, right.
So when I'm describing exact numbers, I'm describing them
as having infinite sig figs.
And why is that right?
We talked about this.
Because it's defined.
Okay. So we should report our final answer to 2 sig figs,
so it's going to take about 260 minutes for the patient
to receive their morphine dose.
All righty.
So that concludes our dosage calculation practice.
So I encourage you to take the time now
to work several practice problems
to reinforce your understanding
so that you do well in your coursework.