Lesson video

Hello, my name is Dr.

Rowlandson, but I'm not the kind of doctor that we're going to be talking about in today's lesson, 'cause today we're going to be looking at some of the maths that is used in medical professions.

So let's get started.

Welcome to today's lesson from the unit of maths in the workplace.

This lesson is called medical professional, and by the end of today's lesson, we will understand how maths is used by medical professionals.

Here are some previous keywords that will be useful during today's lesson, so you may want to pause the video if you need to remind yourself what any of these words mean, then press play when you're ready to continue.

The lesson is broken into three learning cycles, where each one looks at a particular situation where maths is used by medical professionals.

I should stress that these are not the only situations where math is used.

These are just three examples to give you a flavour.

So let's start by looking at a case where arithmetic is used in medical professions.

When a patient is in hospital and they are being closely monitored, nurses may keep a record of the amount of fluid that enters and leaves their body.

Fluids entering the body include things such as drinks and liquid medication, which is called IV medication.

The IV means intravenous, in other words is medication that goes into the patient's veins.

It also includes IV fluids and blood transfusions.

Fluids leaving the body include not so nice things, such as urine, vomit and fluid drains.

Now the nurses are keeping a record of all the fluid that goes into the body and all the fluid that leaves the body, and this information is used to calculate a fluid balance.

The fluid balance may either be positive or negative.

I wonder if you can think what each of these may indicate.

A positive number would indicate that more fluid has entered the body than left it, and a negative number would indicate that more fluid has left the body then entered it.

So let's take a look at an example together.

A nurse is examining a patient's fluid balance chart.

So here we have parts of a fluid balance chart.

We have some columns which indicate the input, so they are fluids that go into the body.

We can see drinks, liquid medication and IV fluids, which are all measured in millilitres.

And we have some columns which show the output, that is fluid that has left the body, urine, vomit or aspiration and drains, and they are also measured in millilitres.

In the far right, we have a column for fluid balance, that's the overall fluid balance again measured in millilitres.

We have a row with some information on about a patient.

This shows all the fluid that's entered and left the body in a period of time, for example, an hour.

Let's calculate this patient's fluid balance.

We could do this by breaking it into small steps.

We could first calculate the amount of fluid that has entered the body by doing 100 plus 500 to get 600.

We could calculate the amount of fluid that has left the body by doing 100 plus 20 to get 120.

And then if we know that 600 millilitres has entered the body and 120 millilitres has left the body, we can calculate the overall fluid balance by doing 600 subtract 120, which gives 480 millilitres as this patient's fluid balance for this period of time.

And that means that the patient's fluid balance is positive.

So let's check what we've learned.

Here, we have another row of information on a patient's fluid balance chart.

Could you please calculate this patient's total input? Pause while you write your answer down, and press play when you're ready to see what it is.

We could add together the two amounts which are in the input columns, 150 plus 10 to get 160 millilitres.

Could you now please calculate the patient's total output? Pause while you right your answer down, and press play when you're ready to see what it is.

If we add together the amounts of fluid that have left the patient's body, we'll do 200 plus 10 to get 210 millilitres.

So could you please now calculate the patient's overall fluid balance for this period of time? Pause while you do it and press play when you're ready for an answer.

We could do the input, subtract the output to get negative 50 millilitres, which means the patient's fluid balance is negative.

Okay, it's over to you then for task A.

This task includes one question and here it is.

We have a table that shows a patient's fluid input and output records during four hours.

Could you please, in part A, calculate the fluid balance for each individual hour, and for part B, calculate the overall fluid balance for the entire four hour period? Pause while you do that, and press play when you're ready to see the answers.

Okay, let's see how we got on with that.

At nine o'clock, the fluid balance was 320 millilitres.

At 10 o'clock, it was negative 190 millilitres.

At 11 o'clock, it was negative 90 millilitres.

And at 12 o'clock, it was 265 millilitres, which means in part B, the overall fluid balance in the entire four hour period was 305 millilitres, which means the fluid balance was positive.

Well done so far.

Let's now look at a case where formula is used in medical professions.

When a patient is in hospital, they may be prescribed drugs.

The amount that is prescribed differs depending on the patient's condition and also the drug that is being used.

Some drugs may be given as tablets, and others may be given as liquid medication.

When liquid medication is used, it's not necessarily all given in one go.

Liquid drugs may be given gradually over a period of time by using an intravenous drip, which is referred to as an IV drip.

The rate at which a drug is given through a drip can depend on many factors, such as the amount of drug that is required, the period of time where it's being administered, and also the mass of the patient themself.

These values can be calculated by using some formula.

So let's take a look at an example.

Amiodarone is a drug that can be used to treat some heart conditions.

In this example, a patient is prescribed 900 milligrammes of amiodarone.

The drug comes in vials, and the amount of drug in each vial is 150 milligrammes, and the volume of liquid in each vial is three millilitres.

We can use this formula on the screen here to calculate the drug dosage that is required.

We have the drug dose is equal to the amount of drug that is prescribed in milligrammes, divided by the amount of drug in each vial in milligrammes, all multiplied by the volume of each vial in millilitres.

Now, if you're not quite sure about what all this means in the context of this situation, don't worry about it.

You can leave it to the professionals for now.

But what we can do is look at how we can use the information that is given to us and the formula that is shown here to perform some calculations.

And Izzy is going to help us.

You may notice that on the left where it says drug dose, it doesn't have any units yet.

Well, Izzy says, "The units for the drug dose will be in millilitres." Can you see why? When we look at the calculation on the right hand side, we can see we have milligrammes divided by milligrammes multiplied by millilitres.

And when we do milligrammes divided by milligrammes, they will cancel out, and we're left just with the millilitres.

Izzy then says, "I can substitute in the values from the information to calculate the required drug dose." Let's do that.

We can do 900, which is the amount prescribed in milligrammes, divided by 150, which is the amount of drug in each vial in milligrammes, multiplied by three, which is the volume of each vial in millilitres.

And when we do that calculation, we get 18 millilitres, which means 18 millilitres of liquid will be required so that the patient receives 900 milligrammes of this particular drug.

Let's now take a look at this formula a little bit more closely, because it can be interpreted in different ways for this particular context.

For example, Izzy says, "In this particular case, with the way that the formula is currently arranged, the division calculates the number of vials required to administer 900 milligrammes of the drug." That means when we do 900 divided by 150 to get six, that six means we need to use six vials.

And then the multiplication tells us how much liquid is in six vials.

If there are six vials and each one contains three millilitres, that means altogether we administer 18 millilitres.

So that's how we can interpret this formula with how it's arranged here.

But Izzy says, "If we rearrange the equation, then we could interpret its components in a different way." For example, now we can see we're doing the volume of each vial divided by the amount per vial, multiplied by the amount prescribed.

In this arrangement, the division tells us what volume of the vial will be needed to administer one milligramme of drug.

So in this case, we would first divide three by 150, and that would tell us that 0.

02 millilitres of the liquid that's in the vial would provide one milligramme of the drug.

So then the multiplication would scale this up to get 900 milligrammes of the drug.

We'll do 0.

02 multiplied by 900 to get the same answer again, 18 millilitres will provide 900 milligrammes of the drug.

So let's check what we've learned with an example for you.

A patient is prescribed 600 milligrammes of amiodarone.

The amount of drug in each vial is 150 milligrammes, and the volume of liquid in each vial is three millilitres.

Could you please use the formula you can see on the screen to calculate the drug dose required for this patient? Pause while you do it and press play for an answer.

If you do 600 divided by 150 and multiply by three, you get 12 millilitres.

So if we need to administer 12 millilitres of this drug, how many vials of drug would be required? Pause while you write down an answer, and press play when you're ready to see what it is.

Well, there are a couple of different ways you can calculate this.

One is to look at the fraction you can see in your formula, by doing 600 divided by 150, and that will tell you you need four vials of this drug.

Or another way you can think about it is you know you need to give 12 millilitres of drug to the patient, and each vial has three millilitres in, so you can do 12 divided by three, and that'll tell you you need four vials as well.

Let's now go back to the example that we were working through together earlier.

The patient requires 18 millilitres of amiodarone.

The drug needs to be diluted in a bag with some fluid before it's given, and the total volume in the bag should be 50 millilitres after it has been diluted.

So how much of the fluid is required? Well, to calculate this, we could work out the difference between the amount of drug that's in the bag already and the total volume of the bag after it's been diluted by doing 50 subtract 18 to get 32.

So we'll need 32 millilitres of fluid.

Sometimes the amount of drug that is required cannot be given to a patient all at once.

It may need to be given gradually over multiple hours.

And the amount of drug that is given per hour is referred to as the administration rate.

In our example, the patient is given a 50 millilitre bag of diluted amiodarone over 24 hours.

So what is the administration rate in this situation? We can calculate that by dividing the volume of the bag by the number of hours where it's administered.

In this case, it would be 50 divided by 24, which means the patient should be given 2.

083 recurring millilitres per hour.

However, in this context, the drug is administered to the patient by a machine, and the machine can't quite be as precise as what we've written here.

The machine that administers the drug can only be programmed using amounts given to one decimal place.

So the amount needs to be rounded.

So in this case, it would be 2.

1 millilitres per hour.

Let's now think a bit more about this machine that has given the drug to the patient.

When a drug is administered continuously by an IV drip, the settings of the drip are adjusted according to various factors, including the patient's mass.

It is calculated using the formula we can see on the screen here, just a bit complex when you take into account all the units.

On the left, we have the subject of the formula, which is the drip settings.

And we calculate that by doing first the product of the administration rate, which is in millilitres per hour, multiplied by the amount of drug prescribed, which is in MCG, that is micrograms. A microgram is one millionth of a gramme.

And we divide that by the product of the bag volume in millilitres, the patient's mass in kilogrammes and 60.

And when we calculate that, we get the drip settings, and the units for drip settings is micrograms per kilogramme per minute.

Now, there are a lot of different units and compound units in this formula, which makes it quite complex to look at, but don't worry about that too much if it's bothering you.

What we are going to really focus on in this lesson is finding the values we need from the information that is given, and substitute into the formula to perform the calculation we want.

The main thing we wanna pay attention to with units is whether the units given match the units in the formula.

And sometimes if the information about the drug is given in milligrammes, we may need to convert between milligrammes and micrograms before using the formula.

And one milligramme is equal to 1000 micrograms. So let's apply this formula now to the example that we were working through together.

In this case, the patient was prescribed 900 milligrammes of amiodarone.

It is diluted up to 50 millilitres in a bag.

We calculated that the administration rate is 2.

1 millilitres per hour, and the patient has a mass of 75 kilogrammes.

So what we're going to do is calculate the micrograms per kilogrammes per minute setting for the IV drip, and we can do that by substituting in values from the information into the formula in the appropriate places, and then perform the calculations we need.

Let's start by looking at the top left part of the fraction, which says administration rates in millilitres per hour.

In the information, we can see 2.

1 millilitres per hour, so we can substitute 2.

1 into our formula.

The next part of the fraction says amount prescribed in micrograms. The information says 900 milligrammes was prescribed.

Those units don't quite match yet, so what we need to do first is convert the 900 milligrammes into micrograms by multiplying by 1000.

That's because there are 1000 micrograms in one milligramme.

That means we would get 900,000 micrograms of drug, and that's what we'll substitute into our formula.

And then for the denominator, we can see we want the volume of the bag in millilitres, and that's how it's given to us in the information, so we can substitute 50 in.

We want the patient's mass in kilogrammes, which is how it's given to us in the information, so we can substitute 75 in.

And we're going to multiply by 60 as well.

Now we have all the values in the correct places in our formula, we can calculate to get 8.

4 micrograms per kilogramme per minute as the drip setting.

So let's check what we've learned with an example for you.

I'm gonna break it down to some small steps.

A patient was prescribed 600 milligrammes of amiodarone, and we know that one milligramme is equal to 1000 micrograms. Could you please write down how many micrograms of amiodarone was a patient prescribed? Pause while you do it and press play for an answer.

To convert from milligrammes to micrograms, we multiply by 1000, so we get 600,000 micrograms. At the top of the screen, you can see the formula for calculating the drip settings of the drug, and in the middle, you can see the information about the patient and the drug they're being prescribed.

At the bottom, you can see three fractions.

Which of those fractions shows all the values from the information substituted into the formula into the correct places? Pause while you choose and press play for an answer.

The answer is C.

The administration rate is 2.

1 millilitres per hour.

The amount of drug prescribed was 600,000 micrograms. The bag volume was 50 millilitres, and the patient's mass was 90 kilogrammes, and you multiply the denominator by 60 as well.

Okay, so due now for task A.

This task has one question where it gives you a scenario to work with for yourself, and it's broken into four parts, parts A to D.

The screen now just shows parts A and B of question one.

Pause while do this and press play when you're ready for parts C and D.

Here are parts C and D.

Pause while you do this, and press play when you're ready to go through some answers.

Okay, let's go through some answers.

In this scenario, a patient was being prescribed a drug called rifampicin, and in part A, you had to calculate the drug dose based on information given.

That was 20 millilitres.

In part B, you had to calculate the administration rates.

Well, that would be 166.

7 millilitres per hour.

In part C, you had to convert from the amount in milligrammes to micrograms, which in this case would be 600,000 micrograms. In part B, you had to use information you worked out in parts B and C to calculate the drip settings.

In this case, it would be 37.

04 micrograms per kilogramme per minute.

You're doing great so far.

Let's now move on to the third and final part of this lesson where we're going to look at situation where data is used by medical professions.

One way that medical staff assess a patient's health is by their vital signs.

Vital signs include things such as body temperature, respiratory rate, which is how many breaths a patient takes per minute.

Heart rate, which is how many times a patient heart beats per minute.

And blood pressure, which is the strength that the blood is pushed against a person's arteries as a heart pumps the blood around the body.

Let's take a look at blood pressure.

At the bottom of the screen here, you can see a graph that shows a chart from a blood pressure measurements.

We can see it's a squiggly line showing the patient's blood pressure over time.

A blood pressure measurement has two parts.

One part is called systolic blood pressure, which is abbreviated to SBP.

This is a high number which shows the pressure when the heart squeezes.

On the graph, you can see it's the peaks of the data line.

The other is called diastolic blood pressure, which is abbreviated to DBP, and this is a low number which shows the pressure when the heart relaxes.

That is shown as the low points on the graph.

Blood pressure is usually written as one number over another.

It looks a bit like a fraction, however, this is not a fraction.

It's only notation about blood pressure.

It doesn't mean one number divided by another.

The top number is the systolic blood pressure, and the bottom number is the diastolic blood pressure.

As we said earlier, medical staff look at lots of different vital signs of patients.

However, it'd be quite inconvenient if each of these separate vital signs were displayed on a separate graph.

What can happen is we can have multiple vital signs displayed on the same graph, and that's what we're going to do here.

The horizontal axis shows us five different days of the week, and we have a scale on the vertical axis on the left, and that scale is going to be used to show multiple sets of data.

One set of data will be the heart rate, and each data point is represented by a triangle, which we can see in the key on the label for the axis.

Another set of data will be the respiratory rate, and this will be represented by circles.

And another set of data will be the blood pressure, which is represented by bars or rectangles, where the top of the bar shows the systolic blood pressure, which is a high number, and the bottom of the bar shows the diastolic blood pressure, which is a low number.

Now, all of these vital signs work quite well on the same scale because we can see quite clearly what's going on.

But if we wanted to show the patient's body temperature in degrees Celsius, then that wouldn't quite be so clear on this scale.

Body temperatures don't change by quite so many degrees, so if we plotted the body temperature on this scale, it would look like a straight horizontal line, no matter how much it's increasing or decreasing.

So we're going to want a different scale for body temperature.

But we can still display it on the same graph by placing another vertical scale on the right hand side.

And now we have the patient's body temperature on the same graph, and the data points are displayed by the diamond shapes or the squares which have been rotated 45 degrees.

And to read off those measurements, we'll use the scale on the right hand side where the label "body temperature" is.

So let's see how well we can interpret this graph now with some questions for you to try.

What was the patient's heart rate on Monday? You're going to need to use the key to select the right data from the graph, and then select the right scale, whether it's the left scale or the right scale, and then check the label to see what units to write as well.

Pause while you do this and press play for an answer.

To find the patient's heart rate, we only want to look at the triangles, and then we want to look at Monday.

And then the scale we want to use is the one on the left hand side, because that's the one which is labelled heart rate.

And we can see that is 80, and the units is beats per minute.

What was the patient's respiratory rate on Wednesday? Pause the video while you write down your answer, and press play when you're ready to see what it is.

This time we are looking at the circles for data.

We want to see Wednesday, and we are still using the left hand scale, and we have 20 breaths per minute.

What was the patient's body temperature on Thursday? Pause the video while you write down your answer, and press play when you're ready to see what it is.

Body temperature is displayed with the diamond data points.

We are looking at Thursday's data, but this time we're going to look at a scale on the right hand side 'cause that's the one which is labelled body temperature.

And we can see it's 39 degrees Celsius.

What trend can be observed in the patient's blood pressure? Is it A, decreasing, B, increasing, or C, staying the same? Pause the video while you choose, and press play for an answer.

For this, we want to focus on the rectangles or the bars.

We can see that the blood pressure is increasing over the week.

Okay, it's over to you now for task C.

This task has one question split into six parts, parts A to F.

In this question, you are presented with a patient's vital signs displayed on a single graph, and you have some questions to answer about this data.

Parts A to D are displayed on the screen at the moment.

Pause the video while you do these, and press play for parts E to F.

And here are parts E and F.

Pause the video while you do this, and press play for some answers.

Okay, let's see how we got on then.

In part A, the patient's respiratory rate was at its lowest on Wednesday, which we can see by the data represented by circles.

In part B, the patient's heart rate on Tuesday was 84 beats per minute, which you can see by the data points represented by triangles.

For part C, Lucas thinks their body temperature was 155 degrees Celsius on Monday, and you had to say what mistake Lucas had made.

Well, it looks like Lucas used a scale on the left hand side, rather than the scale on the right hand side.

So in part D, what was the actual body temperature on Monday? It was 39 degrees.

You can see that from the diamond shaped data points and looking at the scale on the right.

In part E, you had to describe the trend of the blood pressure over the five days, and that is looking at the rectangles or the bar shapes, and seeing generally what is happening over the time.

The patient's blood pressure gradually decreased over the five days.

If you word that in any other way that implies that it's decreasing, absolutely well done.

Then part F, you're told that a healthy blood pressure recording is around 120 over 70, and you had to identify on what day or days was the patient's blood pressure around those levels.

Well, Friday matches exactly 120 over 70, so Friday is a definite.

You may also have noticed that the patient's blood pressure is quite close to this on Thursday and Wednesday as well.

Fantastic work today.

Now let's summarise what we've learned.

Jobs in the medical profession may require the use of formulae and calculations.

For example, the correct drug dosage for a patient must be correctly calculated, and there are formulae for how to calculate this.

Interpreting data is also a vital skill for medical staff.

For example, graphs showing a patient's vital sign may be interpreted to determine a course of action.

Well done today.

Have a great day.