Dose Calculations Based on Body Surface Area

How to Calculate Body Surface Area-RxCalculations

If you are a pharmacy student or healthcare professional, you are aware that calculating drug doses is a crucial activity requiring precision and accuracy. Some drugs have set dosages based on age or weight, whilst others require a more nuanced approach.

In this blog post, you will learn how to perform dosage calculations based on body surface area. It has been established that treatment using doses based on body surface area provides the most accurate dose-response relationship for medications with considerable toxicity, making it particularly applicable to chemotherapy and pediatric patients.

More specifically, you will learn how to calculate body surface area using equations and nomograms. You will also see several carefully chosen examples to highlight the many situations in which calculating drug doses based on body surface area may be applied.

By reviewing the content in this post, you will have a comprehensive grasp of how to perform dose calculations based on body surface area and why it is such an important aspect of calculating drug doses. There are three ways you may interact with the material. You may watch the video, listen to the podcast, or read the transcript.

Dose Calculations Based on Body Surface Area (BSA)

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Video Transcription

I'm going to show you how to calculate drug dose based on body surface area.

Drug Dosage Based on Body Surface Area - RxCalculations

Hello, this is Dr. Danquah. So in this tutorial, I'm going to give you a brief overview on why body surface area is important when it comes to drug dose calculations.

We're going to go ahead and look at how you actually determine or calculate the body surface area with some examples, and then we'll finish off with four carefully selected examples illustrating some of the various ways in which you would encounter drug dose calculations based on body surface area.

When it comes to selecting the appropriate dose of medication for a patient, normally the indication of the medication provides sufficient information on how much to give the patient. So, for example, the adult dose for acetaminophen is 650 mg every 4 to 6 hours. So this would be appropriate for most people. There are, however, some drugs that are actually dosed based on the body weight. And I do have a video on calculating drug dosed based on body weight.

Drug Dosage Based on Body Surface Area -RxCalculations

However, there are some therapeutic agents, especially those with significant toxicities, which are best dosed on the body surface area. And the reason is that calculating drug dose based on body surface area has been shown to give the best dose-response relationship for these therapeutic drugs.

Drug Dosage Based on Body Surface Area_RxCalculations

Now, the body surface area method of calculating drug doses is best suited for two scenarios. The first being chemotherapy, where cancer patients received antineoplastics. 

And the second is for pediatric patients. Now, the body surface area is expressed as meters squared, and the normalized dose would then be given typically as milligrams per m2.

So anytime you see the m2 in the denominator, that would be a dose that has been normalized to the body surface area. There are two ways in which you can calculate the body surface area.

The first one is using an equation, and there are about 19 different types of equations that can be used for calculating the body surface area. The more common ones are the Mosteller Method and the Du Bois Method.

Now out of these two, the Mosteller method is more commonly used because the Dubois method or Du Bois formula has been shown to underestimate the body surface area when it comes to pediatric patients.

Aside the equation, the other way you could calculate the body surface area is to use Nomogram. We'll take a look at how you calculate the BSA using the equations and nomograms in this particular tutorial.

Now the last point I like you to have stencilled on your mind from this brief overview is that for an average size adult, the BSA is 1.73 m2. Now let's go ahead and take a look at how you calculate the Body Surface Area using the equation method.

Calculating Body Surface Area Using the Mosteller Equation

Drug Dosage Based on Body Surface Area-Mosteller Equations_RxCalculations

The equation we want to focus on is the Mosteller Method, and the equation says that BSA in m2 is equal to the square root of the patient's height in centimeters times the patient's weight in kilograms divided by 3,600.

Now, the 3,600 is an empirically determined constant, and this number, although the units are not given in the equation, actually has units of centimeter kilogram per meters to the power of 4. Now, this is one form of the equation.

There is an alternative form and that is given as BSA in meters squared is equal to the square root of the patient's height in inches times the patient's weight in pounds divided by 3131.

 Once again, the 3131 is an empirically determined constant and in this scenario has units of inches pounds per meters to the power of 4.

You have two forms of the equation, and my recommendation is for you to use the equation that allows you to get the BSA in the most expeditious manner based on the patient information provided.

The important point to note is that the body surface area depends on the patient's weight and height. Now let's take a look at some examples and see how to do that.

Example 1

Drug Dosage Based on Body Surface Area-Example 1_RxCalculations

In example one, the question says, calculate the body surface area for a patient who weighs 70 kg and is 167.6 cm tall.

Based on the height, which is in centimetres and the weight which is in kilograms, the most appropriate form of the equation to use would be BSA in meters squared, being equal to the square root of the patient's height in centimetres, times the patient's weight in kilograms, divided by the 3600.

Because the units in the equation are the same as the units for the patient information provided. Now we can go ahead and simply substitute the values of the patient's height and the patient's weight into the equation. Now we have BSA in m2 being equal to 167.6 times 70 divided by 3600.

 This breaks down to give us square root of 11,732 divided by 3,600. The BSA in m2 is going to be equal to square root of 3.259, and that should give us 1.81 m2. Let's take a look at another example.

Example 2

Drug Dosage Based on Body Surface Area-Example 2_RxCalculations

This question says, calculate the body service area for a patient who weighs 144 lb and is 68 inches tall. Now, based on the patient information provided, the most appropriate form of the Mosteller equation to use would be BSA in m2 being equal to the square root of patient's height in inches times the patient's weight in pounds divided by 3131.

And the reason being, once again, that the units that we have in the equation match exactly with the units of the patient information provided. So that would allow us to determine the BSA very quickly.

So we go ahead and determine BSA in meters squared, which is going to be equal to the square root of 68, which is the patient's height times 144 lb, which is the patient weight divided by 3131.

And that should be equal to the square root of 9,792, divided by 3131. And That implies that the BSA in meters squared is going to be equal to the square root of 3.127. That should be equal to 1.77 m2.

Example 3

Drug Dosage Based on Body Surface Area-Example 3_RxCalculations

Now, let's take a look at another example. And in this example, the question says, calculate the body surface area for a patient who weighs 180 lb and is 6'3 tall. Now the question becomes, which form of the Mosteller equation do you use here?

Now you could use either form of the equation, but my recommendation, especially if you want to determine the BSA expeditiously, is to use the version of the equation in which the units of the patient's weight, matches the units of the patient's weight given in the question.

So for this scenario to be the one where you have patients' weight in pounds and height in inches. So what that will mean then is we need to convert the 6'3 to inches before we can proceed with that equation.

Drug Dosage Based on Body Surface Area-Example 3_-RxCalculations

So we do a quick conversion for 6 feet. If we want to convert that to inches, we need to use the conversion factor where 1 ft contains 12 in. So the feet cancel out and you end up with 72 in.

But it don't stop here because the patient is 6’3 tall, so we need to add 3 in to that. So the patient's height will be 72 in plus 3 in, which gives us 75 in. So now we go ahead and we put that in this equation, which is the BSA m2 is equal to the patient's height in inches, times the patient's weight in pounds, divided by 3131.

Now we go ahead and substitute the information into the equation. BSA in m2 is going to be equal to the square root of 75, which was the patient's height in inches, which we just calculated, times the 180 lb, which is the patient's weight, divided by 3131.

This should give us the square root of 13,500 divided by 3131, which would then give us BSA in m2 being equal to the square root of 4.312, and that is actually equal to 2.08 m2. So by using this form of the equation, we actually arrived at the BSA in about five steps.

Example 4

Drug Dosage Based on Body Surface Area-Example 4_RxCalculations

So now let's take a look at the next example, which actually is the same question we just looked at in this example, but we are going to use the other version of the Mosteller Equation.

So the question once again says, calculate the body surface area for a patient who weighs 180 lb and is 6'3 tall. For the other version of the Mosteller equation, we need patient's height to be in centimetres and patient's weight to be in kilograms.

We actually need to convert the 6'3 into cm. So the 6 ft, if you want to convert that into inches, is going to be 1 ft contains 12 in, which gives us 72 in. We then go ahead and add the 3 in to that. So we have 72 in plus 3 in that gives us 75 in.

We now need to convert the 75 in into cm. So we have 75 in, we multiply that by the conversion factor where one inch is equivalent to 2.54 cm, the inches cancel out and you end up with 190.5 cm. And so the patient's height is 190.5 cm.

 We now need to convert the weight from pounds to kilograms. So we take the 180 lb, we multiply that by the conversion factor, which says 2.2 pounds is equivalent to 1 kg. The pounds cancel out, and you end up with 81.82 kg. So the patient's weight is 81.82 kg.

Drug Dosage Based on Body Surface Area-Example 4_-RxCalculations

So now we can go ahead and substitute the patient's height in centimeters and the patient's weight in kilograms into the Mosteller Equation. So patient's height is 190.5 cm, the patient's weight is 81.82 kg.

And so now we use the equation which says BSA in meters squared is equal to the square root of the patient's height in centimeters, times patient's weight in kilograms, divided by 3,600.

So we go ahead and put in the values into the equation. BSA in m2 is equal to the square root of 190.5 times 81.82, which is the patient's weight in kilograms divided by 3,600.

This should be equal to the square root of 15,586.71 divided by 3,600, which implies that the BSA m2 is equal to the square root of 4.330, and that should be equal to 2.08 m1. So we notice that the BSA is 2.08 m2, regardless of the version of the Mosteller Equation used.

However, if we compare the number of steps it took to get to the answer, we will notice that it took us about five steps when we used the version that had the patient's height in inches and weight in pounds, compared to about seven steps where the patient's height was in centimetres and the patient's weight was in kilograms.

So you could use either version of the Mosteller equation to determine the BSA. However, if speed is of importance to you, you want to be strategic in the version that you select so that you can arrive at your answer expeditiously. So we talked about how you can use the equation to determine BSA.

Calculating Body Surface Area (BSA) Using Nomograms

Drug Dosage Based on Body Surface Area - Nomograms -RxCalculations

Now let's take a look at how you can use nomograms because every now and then you may be required to use the nomogram to calculate the body surface area of a patient.

So the nomogram is a graphical representation of one of the equations that have been empirically developed to determine body surface area. So a nomogram has three columns. The first is height, which is expressed in centimetres and in inches. The second is the body surface area expressed in meters squared or square meters.

And the third is weight, expressed in kilograms and in pounds. So how do you use the nomogram? You need to know the patient's height, and then you mark that on the normal gram, and then you need to know the patient's weight.

You also mark that on the nomogram, and then you draw a straight line connecting the height and then the weight. And then where the line intersects the BSA column, that would be the BSA or the body surface area of the patient.

Drug Dosage Based on Body Surface Area -Nomograms -RxCalculations

Let's see what all of this looks like, practically speaking. This is how your normal gram looks like.

The height is in the left column and you notice that you have units of centimetres on the left side and units of inches on the right side.

Then the body surface area is right down the middle with units in meters squared and then you have the patient's weight, which is the column to the right and it has units of pounds on the outer side and units of kilograms on the inner side.

Example 5

Drug Dosage Based on Body Surface Area-Example 5_RxCalculations

Now let's take a look at an example of how you can use the nomogram to calculate the body surface area for a patient.

Here the question says, calculate the body surface area for a patient who weighs 170 lb and is 181 cm tall. The first thing we need is the patient's height, which is 181 cm, and then we also need the patient's weight, which is 170 lb.

We go to the nomogram, and then we look for the height column, which will be the column to the left. Because the units of the patient's height are in centimetres, we are looking to the left side of that column.

Drug Dosage Based on Body Surface Area-Example 5_-RxCalculations

We look for the 181 cm and we indicate that on the chart. We have that indicated by the red dot.

Drug Dosage Based on Body Surface Area-Example 5_--RxCalculations

Now we go to the weight column, which is the column on the right hand side, and we have the patient's weight to be 170 pounds.

So on the weight column, we're also going to look on the right hand side of that column, which is where the pounds units are. And so we look for 170 and then we mark that on the nomogram. We just did that with a dot.

Drug Dosage Based on Body Surface Area-Example 5_---RxCalculations

And now what we do is we connect those two dots indicating the height and the weight with a straight line.

And where that straight line crosses the body surface area column, which is the column in the middle, that will give us the body surface area. Here we see that where it crosses the body surface area is just indicated with a red dot, and that gives us the BSA, which would be 1.97 m2.

Example 6

Drug Dosage Based on Body Surface Area-Example 6_RxCalculations

Now let's take a look at another example which says, calculate the body surface area for a patient who weighs 118 kg and is 5'8 tall. We have the patient's weight in kilograms, but then the height is in feet and inches. And in the nomogram, there's no feet on there.

So the first thing that we need to do is convert the height from feet and inches into inches. So we'll take the five feet and we'll convert that to inches.

Using the conversion factor that 1 ft is equivalent to 12 in, the feet cancel out and we end up with 60 in. But we don't stop here because we have 5 ft 8 in. The patient's height is actually going to be equal to the 60 in plus the 8 in, and that gives us 68 in.

Drug Dosage Based on Body Surface Area-Example 6_-RxCalculations

Now we can go ahead and use the nomogram. We have the patient's height to be 68 in, and then the patient's weight is 118 kg. We have the patient's height to be 68 in.

Drug Dosage Based on Body Surface Area-Example 6_--RxCalculations

We go to the height column, which is the column on the left, and we locate 68 in, which will be on the inner side of that column. So we locate 68 in and we indicate that with a dot.

Drug Dosage Based on Body Surface Area-Example 6_---RxCalculations

And then we go to the weight column, which is the column on the right-hand side, and we locate 118 kg. So the kilogram portion is on the inner side of the column. And so we look for 118, and then we indicate that with a dot.

Drug Dosage Based on Body Surface Area-Example 6_----RxCalculations

So now the next thing that we need to do is draw a straight line that connects those two dots. And wherever the straight line intersects the body surface area column, that would be the BSA. So we can indicate that also with another dot and now BSA is equal to 2.28 m2.

Example 7

Drug Dosage Based on Body Surface Area-Example 7_RxCalculations

Now let's take a look at another example. In the previous two examples that we just looked at, the question was more focused on an adult patient. Let's see how it looks like if you do have an adolescent patient.

 Here the question says, calculate the body surface area for an adolescent patient who weighs 90 lb and is 50 in tall. The patient's height is 50 in and the patient's weight is 90 lb.

Drug Dosage Based on Body Surface Area-Example 7_-RxCalculations

The first thing that we do is we take the 50 in and we try and locate that on the height column, which will be the column to the left.

Since we are looking for the patient's height and inches, it's actually on the inner portion of the height column. So we look for 50 in and we indicate that with a dot.

Drug Dosage Based on Body Surface Area-Example 7_--RxCalculations

And then we take the patient's weight, which is 90lb, and we go to the weight column, which is the column on the right hand side. And since the patient's weight is in pounds, it's actually going to be on the outer side on the right hand side of the weight column. So we locate 90 lb and we indicate that with a dot as well.

Drug Dosage Based on Body Surface Area-Example 7_---RxCalculations

So now we connect those two dots with a straight line and wherever the straight line intersects the body surface area, which is the column in the middle, that would be their body surface area.

 And so we can indicate that point of intersection with the dot. And so the body surface area is going to be equal to 1.16 m2. So we looked at how to calculate the body surface area using the Mosteller equation and using nomograms.

4 Strategically Selected Examples of Calculating Drug Dose Based on Body Surface Area

Question 1

Drug Dosage Based on Body Surface Area - Question 1 -RxCalculations

Now we're going to take a look at four strategically selected examples of calculating drug dose based on body surface area.

So let's take a look at this question which says a patient's weight is 70 kg and height is 155 cm. Calculate the dose of fluorouracil in milligrams for the patient if the oncologist orders 400 mg/m2 daily.

Let's quickly analyze this question. What we have is a normalized dose of 400 mg/m2. Since it is per meter squared means this dose has been normalized to body surface area. We need to look out from the question for body surface area information.

Now, since that is not given to us directly, we take a look at the patient's information and we see that we have a height of 155 cm and a weight of 70 kg. So because the units of weight is kilograms and the units of the height is centimetres, we will use this version of the Mosteller equation.

And that version will be your body surface area, BSA, is equal to the square root of the height in centimetres times the weight in kilograms divided by 3,600.

 And so we will go ahead and put that information into the equation. We have the square root of the height, which will be 155 times the weight, which will be 70, divided by the 3,600. And so that is going to be equal to the square root of 3.014.

And so the BSA is going to be equal to 1.74 m2. But we don't stop here. So what we now do is we take the normalized dose, which is the 400 mg/m2, and we multiply that by the body surface area, which is the 1.74 m2. So the meter squares cancel out and you end up having 696 mg.

Question 2

Drug Dosage Based on Body Surface Area - Question 2 -RxCalculations

Let's take a look at another example. So this question says DD is a 20-year-old male who takes phenytoin 150 mg/m2 twice daily for seizures. DD has BSA of 1.1 and the unit should be m2. Phenytoin comes in 50 mg per 5 mL. How many ml will DD need for his daily dose?

So let's quickly analyze this question. We have a normalized dose for phenytoin of 150 mg/m2, and that is given twice daily.

Because it's normalized to body surface area, we need some body surface area information, and that is given us in the question explicitly. So that would be the 1.1 m2. So what we need to do is make sure we know what the daily dose is for DD, because we have been given 150 mg/m2 for each dose.

Now, DD takes two doses every day. Now the doses can cancel out. And what you actually have is 300 mg/m2 every single day. And so this implies that the daily dose is actually going to be 300 mg/m2.

So now what we need to do is actually make use of the daily dose, which is a normalized dose, and find out exactly how many milligrams DD gets. And to do that, we will take the daily dose, which is the 300 mg/m2, and we will multiply that by the body surface area, which is 1.1 m2.

The meters squares cancel out and you end up with 330 mg of phenytoin. But the question is asking for quantity in milliliters, and so we make use of the concentration, which would be 50 mg of phenytoin is present in 5 ml, that should be equal to 330 mg divided by some volume, which would be X ml.

So we go ahead and solve for X, which is our unknown, X equals 5 ml, times 330 mg, divided by 50 mg. And so X equals 33 ml.

Question 3

Drug Dosage Based on Body Surface Area - Question 3 -RxCalculations

Let's take a look at another example which says, the drug carboplatin for ovarian carcinoma is administered intravenously at a dose of 360 mg/m2, except in patients with impaired kidney function, in which case the dose is reduced by 30%. How many milligrams of the drug should be administered to a renally impaired patient measuring 5'2" and weighing 110 lb.?

Let's analyze this question. We have a normalized dose of 360 mg/m2. But this patient has impaired kidney function and so the dose is reduced by 30%. We need to account for that as we solve this particular question.

But because it's normalized to m2, which is body surface area, we need BSA or Body Surface Area information. Since that is not given us directly, we make use of the patient information. We have weight of 110 lb and height of 5'2.

Since we have the patient's weight in pounds, so the most appropriate form of the equation that we will use is BSA is equal to the square root of height in inches, times the weight in pounds, divided by 3131.

Now, the weight is already in pounds and that's why we are using this form of the equation. But we need to convert the height to inches. So for patient's height, we will have 5 ft, and we'll convert that to inches using the conversion factor, 1 ft is equivalent to 12 in.

The feet cancel out and end up with 60 in. But now we don't stop there, we added 2 in because the patient is 5'2, so plus 2 in, and that gives us 62 in. So now we can go ahead and plug the information into the equation. So BSA is going to be equal to the square root of 62 times 110, divided by 3131.

And that should be equal to the square root of 6820 divided by 3131, which is equal to the square root of 2.178, which is equal to 1.48 m2. So now we have the body surface area. The next thing we want to do is actually determine the normalized dose for this particular patient.

So we will take the 360 mg/m2, and we need to adjust this because the patient has impaired kidney function. And so since that is reduced by 30%, it means we need to give 70% of the actual dose.

 And now 70 divided by 100 is going to be equal to 0.7. So we can multiply the normalized dose by 0.7, and that should be equal to 252 mg/m2. So to determine the actual dose, we'll take the normalized dose, which is the 252 mg/m2, and multiply that by the body surface area, which is the 1.48 m2, and that should be equal to 372.96 mg.

Question 4

Drug Dosage Based on Body Surface Area - Question 4-RxCalculations

Let's take a look at another example which says a patient is at the clinic to get his round of chemotherapy. His medication is dosed at 110 mg/m2 over 4 hours. How much of the drug in milligrams is a patient getting every hour if his BSA is 1.9 m2? Let's analyze the question.

We have a dose of 110 milligrams per meter squared over 4 hours. So that is given over 4 hours. And because it's normalized to meter squared, which is body surface area, we need to make sure we have BSA or Body Surface Area information. And now the question actually tells us that his BSA is 1.9 m2. So we don't need to calculate the BSA here.

But what we need to do is we need to take the 110 mg/m2, which is given over 4 hours, and determine what it should be for 1 hour. So we multiply that by 1 hour, the hour cancels out, and that actually gives us 27.5 mg/m2.

So we can go ahead and find the amount in milligrams that the patient is getting by taking the 27.5 mg/m2 multiplying that by the body surface area, which is 1.9 m2. So the meter squares cancel out and we end up with 52.25 milligrams.

 So I hope you found this tutorial useful. Thank you so much, and I will see you in the next blog post.

Frequently Asked Questions

What is Body Mass Index (BMI)?

Maintaining a healthy body weight is critical for your overall health. But how do you know if you're at a healthy weight? That's where Body Mass Index, or BMI, comes in. BMI is a useful tool for assessing your body weight and determining if it falls within the “normal” range. Here’s what you need to know about BMI and why it matters. 

What Exactly Is BMI? 

BMI stands for body mass index, which is an estimate of your total body fat based on your height and weight. It’s calculated by dividing your weight in kilograms by your height in meters squared (kg/m2).

The resulting number is used to determine whether someone is underweight, normal weight, overweight, or obese. The World Health Organization (WHO) has developed the following categories to help classify someone's BMI: 

• Underweight: Less than 18.5 

• Normal Weight: 18.5–24.9 

• Overweight: 25–29.9 

• Obese: 30 or higher

Why Is BMI Important? 

BMI can be a useful tool for assessing whether someone is at a healthy weight or not. However, it should not be used as the sole indicator of health status since it does not take into account muscle mass or other factors that may influence one's health such as age and lifestyle choices like smoking and alcohol consumption.

Also, athletes who have a large amount of muscle may have a falsely elevated BMI due to the fact that muscle weighs more than fat even though they are considered to be very fit and healthy individuals.

Therefore, any assessment of one's health should take into account multiple factors including diet quality, exercise habits, lifestyle factors, etc., in addition to their BMI score when making determinations about their overall health status.  

BMI can be an important tool for helping assess whether you are at a healthy body weight or not; but it should not be used as the only indicator of one’s health status since there are many other important factors that contribute to overall well-being such as diet quality, exercise habits and lifestyle choices like smoking and alcohol consumption.

Additionally, athletes with large amounts of muscle may have falsely elevated BMIs due to the fact that muscle weighs more than fat; so any assessment of one's health should take all these elements into consideration before making decisions about their overall health status. With this knowledge in hand—you’re now equipped with the basics on understanding Body Mass Index!

How to Calculate BMI

BMI is a measure of body fat and is calculated by dividing an individual’s weight in kilograms by the square of their height in meters.

It gives an indication of whether a person's weight falls within a healthy range for their height. Calculating BMI is a simple process that could prove to be quite beneficial and here is a useful BMI calculator to quickly calculate BMI.

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