Medicine and Math - Math Central
Medicine and Math - Math Central
Medicine and Math
care for people around the world. Doctors and nurses use math when
they write prescriptions or administer medication. Medical
professionals use math when drawing up statistical graphs of epidemics
or success rates of treatments. Math applies to x-rays and CAT scans.
Numbers provide an abundance of information for medical professionals.
It is reassuring for the general public to know that our doctors and
nurses have been properly trained by studying mathematics and its uses
for medicine.
ailments. Prescriptions indicate a specific medication and dosage
amount. Most medications have guidelines for dosage amounts in
milligrams (mg) per kilogram (kg). Doctors need to figure out how many
milligrams of medication each patient will need, depending on their
weight. If the weight of a patient is only known in pounds, doctors
need to convert that measurement to kilograms and then find the amount
of milligrams for the prescription. There is a very big difference
between mg/kg and mg/lbs, so it is imperative that doctors understand
how to accurately convert weight measurements. Doctors must also
determine how long a prescription will last. For example, if a
patient needs to take their medication, say one pill, three times a
day. Then one month of pills is approximately 90 pills. However, most
patients prefer two or three month prescriptions for convenience and
insurance purposes. Doctors must be able to do these calculations
mentally with speed and accuracy.
Doctors must also consider how long the medicine will stay in
the patient’s body. This will determine how often the patient needs to
take their medication in order to keep a sufficient amount of the
medicine in the body. For example, a patient takes a pill in the
morning that has 50mg of a particular medicine. When the patient wakes
up the next day, their body has washed out 40% of the medication.
This means that 20mg have been washed out and only 30mg remain in the
body. The patient continues to take their 50mg pill each morning.
This means that on the morning of day two, the patient has the 30mg
left over from day one, as well as another 50mg from the morning of day
two, which is a total of 80mg. As this continues, doctors must
determine how often a patient needs to take their medication, and for
how long, in order to keep enough medicine in the patient’s body to
work effectively, but without overdosing.
The amount of medicine in the body after taking a medication
decreases by a certain percentage in a certain time (perhaps 10% each
hour, for example). This percentage decrease can be expressed as a
rational number, 1/10. Hence in each hour, if the amount at the end of
the hour decreases by 1/10 then the amount remaining is 9/10 of the
amount at the beginning of the hour. This constant rational decrease
creates a geometric sequence. So, if a patient takes a pill that has
200mg of a certain drug, the decrease of medication in their body each
hour can be seen in the folowing table. The Start column contains the number of mg of the drug remaining in the system at the start of the hour and the End column contains the number of mg of the drug remaining in the system at the end of the hour.
The sequence of numbers shown above is geometric because there
is a common ratio between terms, in this case 9/10. Doctors can use
this idea to quickly decide how often a patient needs to take their
prescribed medication.
Numbers give doctors much information about a patient’s condition.
White blood cell counts are generally given as a numerical value
between 4 and 10. However, a count of 7.2 actually means that there
are 7200 white blood cells in each drop of blood (about a microlitre).
In much the same way, the measure of creatinine (a measure of kidney
function) in a blood sample is given as X mg per deciliter of
blood. Doctors need to know that a measure of 1.3 could mean some
extent of kidney failure. Numbers help doctors understand a patient’s
condition. They provide measurements of health, which can be warning
signs of infection, illness, or disease.
a useful measure. Your BMI is equal to your weight in pounds, times
704.7, divided by the square of your height in inches. This method is
not always accurate for people with very high muscle mass because the
weight of muscle is greater than the weight of fat. In this case, the
calculated BMI measurement may be misleading. There are special
machines that find a person’s BMI. We can find the BMI of a 145-pound
woman who is 5’6” tall as follows.
mathematics is in the use of CAT scans. A CAT scan is a special type
of x-ray called a Computerized Axial Tomography Scan. A regular x-ray
can only provide a two-dimensional view of a particular part of the
body. Then, if a smaller bone is hidden between the x-ray machine and a
larger bone, the smaller bone cannot be seen. It is like a shadow.
It is much more beneficial to see a three dimensional
representation of the body’s organs, particularly the brain. CAT scans
allow doctors to see inside the brain, or another body organ,
with a three dimensional image. In a CAT scan, the x-ray machine moves
around the body scanning the brain (or whichever body part is being
scanned) from hundreds of different angles. Then, a computer takes
all the scans together and creates a three dimensional image. Each
time the x-ray machine makes a full revolution around the brain, the
machine is producing an image of a thin slice of the brain, starting at
the top of the head and moving down toward the neck. The
three-dimensional view created by the CAT scan provides much more
information to doctors that a simple two-dimensional x-ray.
Mathematics plays a crucial role in medicine and because people’s
lives are involved, it is very important for nurses and doctors to be
very accurate in their mathematical calculations. Numbers provide
information for doctors, nurses, and even patients. Numbers are a way
of communicating information, which is very important in the medical
field.
Medicine and Math
Natasha Glydon
Both doctors and nurses use math every day while providing health care for people around the world. Doctors and nurses use math when
they write prescriptions or administer medication. Medical
professionals use math when drawing up statistical graphs of epidemics
or success rates of treatments. Math applies to x-rays and CAT scans.
Numbers provide an abundance of information for medical professionals.
It is reassuring for the general public to know that our doctors and
nurses have been properly trained by studying mathematics and its uses
for medicine.
Prescriptions and Medication
Regularly, doctors write prescriptions to their patients for variousailments. Prescriptions indicate a specific medication and dosage
amount. Most medications have guidelines for dosage amounts in
milligrams (mg) per kilogram (kg). Doctors need to figure out how many
milligrams of medication each patient will need, depending on their
weight. If the weight of a patient is only known in pounds, doctors
need to convert that measurement to kilograms and then find the amount
of milligrams for the prescription. There is a very big difference
between mg/kg and mg/lbs, so it is imperative that doctors understand
how to accurately convert weight measurements. Doctors must also
determine how long a prescription will last. For example, if a
patient needs to take their medication, say one pill, three times a
day. Then one month of pills is approximately 90 pills. However, most
patients prefer two or three month prescriptions for convenience and
insurance purposes. Doctors must be able to do these calculations
mentally with speed and accuracy.
Doctors must also consider how long the medicine will stay in
the patient’s body. This will determine how often the patient needs to
take their medication in order to keep a sufficient amount of the
medicine in the body. For example, a patient takes a pill in the
morning that has 50mg of a particular medicine. When the patient wakes
up the next day, their body has washed out 40% of the medication.
This means that 20mg have been washed out and only 30mg remain in the
body. The patient continues to take their 50mg pill each morning.
This means that on the morning of day two, the patient has the 30mg
left over from day one, as well as another 50mg from the morning of day
two, which is a total of 80mg. As this continues, doctors must
determine how often a patient needs to take their medication, and for
how long, in order to keep enough medicine in the patient’s body to
work effectively, but without overdosing.
The amount of medicine in the body after taking a medication
decreases by a certain percentage in a certain time (perhaps 10% each
hour, for example). This percentage decrease can be expressed as a
rational number, 1/10. Hence in each hour, if the amount at the end of
the hour decreases by 1/10 then the amount remaining is 9/10 of the
amount at the beginning of the hour. This constant rational decrease
creates a geometric sequence. So, if a patient takes a pill that has
200mg of a certain drug, the decrease of medication in their body each
hour can be seen in the folowing table. The Start column contains the number of mg of the drug remaining in the system at the start of the hour and the End column contains the number of mg of the drug remaining in the system at the end of the hour.
| Hour | Start | End |
|---|---|---|
| 1 | 200 | 9/10 x 200 = 180 |
| 2 | 180 | 9/10 x 180 = 162 |
| 3 | 162 | 9/10 x 162 = 145.8 |
| . | . | . |
is a common ratio between terms, in this case 9/10. Doctors can use
this idea to quickly decide how often a patient needs to take their
prescribed medication.
Ratios and Proportions
Nurses also use ratios and proportions when
administering medication. Nurses need to know how much medicine a
patient needs depending on their weight. Nurses need to be able to
understand the doctor’s orders. Such an order may be given as: 25
mcg/kg/min. If the patient weighs 52kg, how many milligrams should the
patient receive in one hour? In order to do this, nurses must convert
micrograms (mcg) to milligrams (mg). If 1mcg = 0.001mg, we can find
the amount (in mg) of 25mcg by setting up a proportion.
administering medication. Nurses need to know how much medicine a
patient needs depending on their weight. Nurses need to be able to
understand the doctor’s orders. Such an order may be given as: 25
mcg/kg/min. If the patient weighs 52kg, how many milligrams should the
patient receive in one hour? In order to do this, nurses must convert
micrograms (mcg) to milligrams (mg). If 1mcg = 0.001mg, we can find
the amount (in mg) of 25mcg by setting up a proportion.
By cross-multiplying and dividing, we see that
25mcg = 0.025mg. If the patient weighs 52kg, then the patient receives
0.025(52) = 1.3mg per minute. There are 60 minutes in an hour, so in
one hour the patient should receive
1.3(60) = 78mg. Nurses use ratios and proportions daily, as
well as converting important units. They have special “shortcuts” they
use to do this math accurately and efficiently in a short amount of
time.
25mcg = 0.025mg. If the patient weighs 52kg, then the patient receives
0.025(52) = 1.3mg per minute. There are 60 minutes in an hour, so in
one hour the patient should receive
1.3(60) = 78mg. Nurses use ratios and proportions daily, as
well as converting important units. They have special “shortcuts” they
use to do this math accurately and efficiently in a short amount of
time.
White blood cell counts are generally given as a numerical value
between 4 and 10. However, a count of 7.2 actually means that there
are 7200 white blood cells in each drop of blood (about a microlitre).
In much the same way, the measure of creatinine (a measure of kidney
function) in a blood sample is given as X mg per deciliter of
blood. Doctors need to know that a measure of 1.3 could mean some
extent of kidney failure. Numbers help doctors understand a patient’s
condition. They provide measurements of health, which can be warning
signs of infection, illness, or disease.
Body Mass Index
In terms of medicine and health, a person’s Body Mass Index (BMI) isa useful measure. Your BMI is equal to your weight in pounds, times
704.7, divided by the square of your height in inches. This method is
not always accurate for people with very high muscle mass because the
weight of muscle is greater than the weight of fat. In this case, the
calculated BMI measurement may be misleading. There are special
machines that find a person’s BMI. We can find the BMI of a 145-pound
woman who is 5’6” tall as follows.
First, we need to convert the height measurement of 5’6” into inches, which is 66”. Then, the woman’s BMI would be:
This is a normal Body Mass Index. A normal BMI is
less than 25. A BMI between 25 and 29.9 is considered to be overweight
and a BMI greater than 30 is considered to be obese. BMI
measurements give doctors information about a patient’s health.
Doctor’s can use this information to suggest health advice for
patients. The image below is a BMI table that gives an approximation of
health and unhealthy body mass indexes.
less than 25. A BMI between 25 and 29.9 is considered to be overweight
and a BMI greater than 30 is considered to be obese. BMI
measurements give doctors information about a patient’s health.
Doctor’s can use this information to suggest health advice for
patients. The image below is a BMI table that gives an approximation of
health and unhealthy body mass indexes.
 Image reproduced with permission of Health Canada |
CAT Scans
One of the more advanced ways that medical professionals use mathematics is in the use of CAT scans. A CAT scan is a special type
of x-ray called a Computerized Axial Tomography Scan. A regular x-ray
can only provide a two-dimensional view of a particular part of the
body. Then, if a smaller bone is hidden between the x-ray machine and a
larger bone, the smaller bone cannot be seen. It is like a shadow.
 Image reproduced with permission of NeuroCognition Laboratory |
representation of the body’s organs, particularly the brain. CAT scans
allow doctors to see inside the brain, or another body organ,
with a three dimensional image. In a CAT scan, the x-ray machine moves
around the body scanning the brain (or whichever body part is being
scanned) from hundreds of different angles. Then, a computer takes
all the scans together and creates a three dimensional image. Each
time the x-ray machine makes a full revolution around the brain, the
machine is producing an image of a thin slice of the brain, starting at
the top of the head and moving down toward the neck. The
three-dimensional view created by the CAT scan provides much more
information to doctors that a simple two-dimensional x-ray.
Mathematics plays a crucial role in medicine and because people’s
lives are involved, it is very important for nurses and doctors to be
very accurate in their mathematical calculations. Numbers provide
information for doctors, nurses, and even patients. Numbers are a way
of communicating information, which is very important in the medical
field.
Another application of mathematics to medicine involves
a lithotripter. This is a medical device that uses a property of an
ellipse to treat gallstones and kidney stones.
To learn more, visit the Lithotripsy page.
a lithotripter. This is a medical device that uses a property of an
ellipse to treat gallstones and kidney stones.
To learn more, visit the Lithotripsy page.
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