Download Part I lecture of Unit 1

RSPT 1325 Sciences: unit 1 lecture/homework page 1
RSPT 1325 Sciences lecture
Part I of Unit 1: Math
By Elizabeth Kelley Buzbee AAS, RRT-NPS, RCP
1.
Be able to calculate percentages
A fraction is a way of comparing two numbers. One number represents the content [what we
actually have] while the other number is the capacity [the total number of items]
Content/capacity = fraction
Complete this table
The fraction
The relationship
You have 10 out of a possible 20.
10/20
You have
out of a possible____
3/4
You have
out of a possible____
4/2 *
*Please note that the last fraction has more in the content than in the capacity. Oddly
enough, in nature we will sometimes end up with a content that is larger than the
capacity.
For example a person with a fast heart rate [tachycardia] has more heartbeat/min
[content] than normal heart/beat [capacity]. If normal high HR is 100 bpm and your
patient has a heart rate of 120, he has 120 parts out of a possible 120.
A percent is a fraction based on 100 parts. 50% is 50/100, 3% is 3/100 and .25% is
.25/100.
1. Obviously, when we discuss numbers, they are rarely in groups of 100, so we need to
convert a percentage of a number into an actual number.
2. To work with a percent, we need to change the percent to a decimal. To do this we take
the fraction created by the percent and divide:
You do these:
Percent
fraction
Decimal
.25/100
.0025
.25%
75%
6%
1.25%
5%
.5%
3. If you need to find 25% of a number, you would multiply that number by .25 because as
we know 25/100 is .25.
4. Example: Tires are on sale for 33% off. The ticket price is $250.
(33/100) x 250 =
.33 x 250
= 82.5.
You have saved $82.5 and only have to pay $167.5.
You do these:
i. Based on the above example: you have to pay 8% tax on these tires based on
their sale price.
1. How much tax will you pay?
ii. Based on the above example: you have a coupon that will give you 10% off the
original [ticket] price.
1. How much more money have you saved?
RSPT 1325 Sciences: unit 1 lecture/homework page 2
2.
What do you pay now? [Don’t forget to refigure the tax]
iii. Here’s a respiratory care application for this math. After you start him on
oxygen mask, your patient has a heart rate that has dropped 25% from his
starting [baseline] rate of 125 BPM [beats/minute]
1. By how many beat/minute has the heart rate dropped?
2. What is the final heart rate?
iv. One way of measuring lung function is to measure the speed of exhaled gases.
After inhaling some medicine, your patient’s peak exhaled flow rate [PEFR]
rises 70% from the baseline of 300 ml/minute.
1. By how many ml/minute has the PEFR risen?
2. What is the new PEFR?
5.
6.
Another way to use percentages is to figure out what percent a number is of another
number.
To do this calculation, first we turn the percentage into a decimal and then multiply by
the number [capacity] then multiply by 100.
Do these:
problem
30 is what
percent of 60?
Turn into a
fraction:
Turn the fraction
into a decimal
Multiply the decimal by
100 to get the percent.
30/60
.5
50%
18 is what percent
of 180?
25 is what percent
of 30?
120 is what
percent of 100?*
* Note that the last problem results in a number higher than 100%
Another way to work with percentages is to figure out what the capacity is when know
what percent a given content is of the unknown capacity.
In other words, if 80 is 40% of a number, what is that number?
RSPT 1325 Sciences: unit 1 lecture/homework page 3
7.
To solve this problem we do the following:
Problem:
Turn percent
Turn the word “of”
into decimal
into multiplication
80 is 40% of what
number?
or
80 = 40% of X
80 = .4 of X
80 = .40 (X)
Solve for X by
dividing both sides by
the decimal
80 /. 40 = .40 ( X)
.40
80/.40 = X
X = 200
80 is 40% of 200
450 is 2% of what
number?
Or 450 =2% of X
3.5 is 75% of what
number?
Or 3.5 = 75% of X
.3 is 12.5% of what
number?
50 is 125% of what
number?
2.
Be able to calculate ratio problems.
1. When we use ratios we are comparing two numbers with the same units. 1:2 is easy to
understand, but most of us find it harder to understand a relationship of 120:2450.
2. Because most of us need to compare something to one in order to understand the
relationship, it is better to reduce the ratio so that one of the numbers equals 1.
3. This action is accomplished by dividing both sides of the ratio by the lower number.
Example
25: 75
25 : 75
25 25
1: 3
You do these:
ratio
1:x
33:66
25.4: 100.5
30:30,000
If the lower number happens to be to the right of the “:”, we still do the formula the same way:
ratio
x:1
88:44
18: 9.7
350:30
RSPT 1325 Sciences: unit 1 lecture/homework page 4
How would we use this skill in Respiratory Care?
If a person is breathing 10 breaths /minute, each breath lasts about 6 seconds [6 seconds x 10 = 60
seconds.] We call this the cycle time.
If the inspiratory phase lasts 2 seconds, what is the ratio of inspiratory to expiratory phase?
[Part I] Inspiratory phase + expiratory phase = 6 seconds [cycle time]
So 2 seconds + x = 6 seconds
6 seconds - 2 seconds = x seconds
Expiratory time is 4 seconds
[Part II] the ratio of inspiratory : expiratory would be
2 seconds : 4 seconds
To reduce this would be:
1:2
You solve the following questions:
1. If the patient’s inspiratory time was 1 second and his expiratory time was 3 seconds, what is his
I:E ratio?
2.
If the patient’s inspiratory time is 1 second and the total breath lasts 2 seconds, what is the I:E
ratio?
3.
Your patient is a newborn baby with an inspiratory time of .25 second and a respiratory rate of 60
bpm [entire breath is 1 second.] What is the I:E?
Each breath has a measurable volume which we call the tidal volume or VT. Part of this VT is
considered ‘wasted’ or ‘dead space’ [VD] because it doesn’t come in contact with the blood stream to
exchange gases. A normal VD/VT ranges between .30 to .40. In other words, 30-40% of a person’s VT
is VD.
Calculate the VD/VT when the VD 100 ml and the VT is 500 ml
100 ml : 500 ml = reduce = 1:5
Convert to fraction, then decimal --- 1/5 = .20
VD/VT = .20
VD in ml
200
150
125
3.
VT in ml
300
650
500
VD/VT
200:300
reduced
2:3 or 1:1.5
VD/VT in decimal
.66
Be able to calculate conversion from liter/minute to liter/second.
1. Respiratory therapists frequently have to measure the speed a patient is breathing. The
units are liter/minute or liter/second.
2. To convert from liter/minute [LPM] to liter/second, we need only divide the liter/minute
by 60 [60 seconds in a minute]
3. To convert from liters/second to liters/minute, we would multiply the liters/second by 60.
4. An easy method to remember this is that when we go from seconds to minutes we
are getting larger time frames so we would have to multiply by 60.
RSPT 1325 Sciences: unit 1 lecture/homework page 5
You do these:
300 Liter/minute
25 liters/second
555 Liters/minutes
4.
liters/second
Liter/minute
liters/second
Be able to work with and convert between different units in the international system
(SI).
In 1960, the scientific community decided to use the same system of units and to use the
metric system. Actually the USA adopted the metric system in 1890s but like Burma, we
have held onto old-fashioned apothecary measurements such as gallons and pints for way,
way too long.
1. Know the units of measurement of mass, volume, length temperature and time.
 For mass we will use grams as the basic unit of measurement.
 For length we use the meter, and for time the second.
 We use liters for volume as the basic unit of measurement.
1.
Know the derived prefixes for the above SI units of measurement.
100 grams = hectogram
100 meters = hectometer
1000 grams = kilogram [kg]
1000 meters – kilometer
1/10 meter = 1 decimeter
1/10 gram = 1 decigram
1/1000 grams = microgram
10 meters = dekameters
10 grams = dekagrams
1/100 meter = 1 centimeter [cm]
1/100 gram = 1 centigram
1/1000 meter = millimeter [ml]
1/1000 gram = milligram [mg]
A trick to remember these prefixes.
You have 100 cents in a dollar. “Centi” means 1/100th of a dollar
A decade is 10 years so deka-meter is 10 meters, but when an ancient Roman
general executed 1/10 of his army for running from the enemy, he ‘decimated’ the
troops. Deci = 1/10th.
When the cops bust someone for “10 Kilo of marijuana” they are quite happy
because they now have 10 x 1000 grams of marijuana. A kilo = 1000
You do the following
Unit of measurement
1/10th
1/100th
1/100th
mass
volume
Length
RSPT 1325 Sciences: unit 1 lecture/homework page 6
Unit of measurement
10
100
1000
mass
volume
Length
hint:
To convert from milligrams to grams, you would divide by 1000 because you are going
from many tiny units to a larger unit.
To convert from liters to ml, you would multiple by 1000 because you are going
from a large unit to many smaller units.
You do these:
1. A person whose body weight [mass] is 65 kg would also weigh --- grams.
2.
A person whose trachea is 23 centimeters long, would also have a trachea that is --meters long.
3.
A person whose VT is .8 Liters, would also have a VT that is – milliliters.
Conversion of metric system to English [apothecary.]



1 meter = 39.37 inches or 3.28 feet
1 kilograms = 2.2 pounds
1 ounce = 28 grams
You do these
If you have:
3 meters
3 milimeters =
You would have:
meters
inches
inches
1.
150 ounces
grams
15 meters
feet
1.5 meters
feet
254 kilograms
pounds
35,000 grams =
kg
pounds
Your patient weights 25 kilograms, how many pounds does he weigh?
2.
Your patient weights 120 pounds, how many kilograms does he weigh?
RSPT 1325 Sciences: unit 1 lecture/homework page 7
Be able to calculate proportions.
a. A proportion is used to compare two different ratios. A proportional relationship
means that the relationships are the same even if the actual numbers are different
b. Example: 3:10 as x : 20
c. To solve this type of problem we would do the following steps:
3:10 as X : 20
3:10 as X : 20
The numbers on the outside are multiplied together, while the numbers on the inside are
multiplied together
3 (20) = 10 (X)
Now solve for X:
60 =
10 X
60 =
10 X
10
10
6=X
3:10 as 6:20
“3 is to 10 as 6 is to 20.”
Ratio A
Ratio B
450:950
35 : X
12.5: 200
X : 950
1: 35.7
X: 87
The numbers on the outside [extremes] are
multiplied together, while the numbers on the
inside [means] are multiplied together
450 : 950 = 35 : X
450 (X) = 950 (35)
450 X = 33,250
450
450
X = 73.8
In respiratory care the therapist may have to figure out an inspiratory time with a
known inspiratory: expiratory ratio [I:E].
If a patient’s I:E is 1:1.5 and the inspiratory time is 1.25 seconds, calculate the expiratory time:
1:1.5 as 1.25 : X
1:1.5 as 1.25 : X
(1)X = 1.5 (1.25)
X = 1.875 seconds
1:1.5 as 1.25 : 1.875
The expiratory time is 1.875 seconds
RSPT 1325 Sciences: unit 1 lecture/homework page 8
You solve these:
If the I:E ratio is:
1:3
The inspiratory time is:
1.5 seconds
The expiratory time is:
1: 4
1:5
6 seconds
1:1.5
4.5 seconds
Another way we use proportions is to calculate drug dosages.
EXAMPLE: Your drug is 1 mg: 1 ml. how many mg are found in 10 ml? We would solve this by
setting up two ratios and solving for X. Make sure that the unit you put on the right is the same
unit placed on the right in the other ratio
1 mg: 1 ml as x : 10 ml
1 (10) = x (1) = 10 mg
1 mg :1 ml as 10 mg : 10 ml
You solve these:
If the ratio is:
When You have:
Then you would have:
1 mg: 2.5 ml
3 mg
ml
2.5 mg : 3 ml
5 mg
ml
45 grams: 150 ml
grams
3000 ml
6 grams: 300 ml
.5 grams
ml
.5 mg: 3 ml
mg.
6 ml
Another example of using ratio is to compare the VD/VT ratio.
If the VD/VT ratio is 1:2 and the VD is 300ml, calculate the VT:
1 : 2 as 300 ml: X
1( X) =2 (300 ml)
X = 600 ml
1:2 is to 300 ml: 600 ml
When the VD/VT ratio is:
1:4
1:2.5
The VD is:
The VT is:
450
500
1:3
1.
200
Your patient has a VD that is 250 and his VT is 500, what is the VD/VT ratio?
2.
Your patient has a VD/VT ratio of 1:3, with a VD of 150; what is his VT?
Still another way that respiratory therapists use ratios is to determine how much
extra oxygen we need to give a patient.
EXAMPLE If we know that a patient gets a Pa02 of 68 torr on Fi02 .21 , we need to find out how
much Fi02 we need to give to increase the Pa02 to 80 torr we could set up a ratio:
Pa02:Fi02 as Pa02 we want : Fi02 we need
68 torr: .21 as 80 : X
68 X = .21(80)
68 X = .21(80)
68
68
X = .247 or
to get a Pa02 of 80 torr we need an Fi02 of .247
RSPT 1325 Sciences: unit 1 lecture/homework page 9
You do these:
Patient Pa02
55 torr
Current Fi02:
.45
45 torr
.35
45 torr
.28
75 torr
.21
1.
We want Pa02:
85 torr
We need Fi02 of:
.5o
65 torr
.45
Your patient has an ABG with a Pa02 of 45 mmHg on Fi02 of .35. If we increase
the Fi02 to .5 what is his predicted Pa02?
2. Your patient has an ABG with a Pa02 of 55 mmHg on Fi02 .60. If we want to
increase his Pa02 to 80 mmHg, what Fi02 do we suggest to the doctor?
3. Your patient is on Fi02 50% and you get an ABG with a Pa02 of 188 mmHg. To
what Fi02 do we adjust this patient to get a Pa02 of 80 mmHg
4. Your patient is extra sensitive to oxygen. If his Pa02 gets above 65 mmHg, he
could just stop breathing. On Fi02 .30, you see that his Pa02 is 45, to what Fi02
do we correct him to get his Pa02 to a safe number?
Be able to calculate proportions.
Directly proportional relationships result in numbers that increase or decrease as their related
numbers increase or decrease.
 Some of the gas laws are direct proportional relationships:
 Charles Law: the relationship between volume of a gas and temperature is directly
proportional when the pressure is constant [k]. For the pressure to stay constant as the
volume rises, the temperature must rise. As the temperature drops the volume drops.
 For the pressure to stay constant, if the volume doubles the temperature must also
double.
V =k
T
Example: if the pressure is constant at 10 cmH20 and the T is 5, calculate the
V
V =k
T
V = 10
5
V (5) = 10 (5)
5
V=50
RSPT 1325 Sciences: unit 1 lecture/homework page 10
V
T
40
20
K [Pressure]
45
45
100
45
200
45
Based on the above table, discuss the relationship between the V and the T
when the P stays the same.
Inverse proportional relationships result in numbers that decrease as the other number
increases, or increases as the other number decreases.
 Boyle’s Law: the relationship between pressure, temperature and volume while the
pressure is constant [k.] As the volume rises, the pressure drops proportionally, as the
volume drops, the pressure rises.
 For the temperature to stay constant, if the pressure doubles, the volume must decrease
by half.
P (V) = k [temperature constant]
Example: If the temperature is constant at 20 degrees, calculate the P
when the V is 15
P (V) = k
P (15) = 20
P (15) = 20
15
15
P = 1.33
Do these:
V
P
k [temperature]
30
35
45
35
60
35
90
35
Based on the above table, discuss the relationship between the V & the P when the
temperature is constant.
Be able to perform dimensional analysis.
When the respiratory therapist has to compare items with different units, we must use
dimensional analysis. Conversion between different units is an example of dimensional
analysis.
To convert between different units you need to know how many of one unit = the
other unit. Then set up a ratio
EXAMPLE You have a patient who weighs 150 pounds; you need to know how many kg he
weighs.
 The conversion from pounds to 2.2 pounds = 1 kg
2.2 pounds : 1 kg as 150 pound: x kg
2.2 x = 1 (150)
X = 150/2.2
RSPT 1325 Sciences: unit 1 lecture/homework page 11
You do these:
Your patient weighs:
235 pounds
His weight in kg:
15 pounds
185 pounds
5 pounds
20 kilograms
45 kilograms





One measurement of pressure is in cmH20; another unit for pressure is mmHg.
The respiratory therapist uses cmH20 for airway pressure and mmHg for blood
pressures, so if data is collected in the ‘wrong’ units, sometimes we must convert
The conversion between these two units of pressure is 1.36 mmHg /1 cmH20.
the conversion from mmHg to cmH20 is .735 cmH20/1 mmHg.
The nice thing about setting up a ratio is that you can use either of the above conversions
because they should mean the same.
You do these:
Your airway pressure is:
20 cmH20
In mmHg, this would be
15 cmH20
45 mmHg
35.5 mmHg
Another common formula used by the respiratory therapist is to calculate the lung compliance
[stiffness] of the lung. The stiffer the lung the more pressure it takes to get a certain volume into
the lungs
C= VT/P
C= 50 ml/10 cmH20
C= 5 ml/cmH20
Do these:
If you have VT:
A. 100 ml
And a P:
25 cmH20
Calculate the C:
ml/cmH20
B.
300 ml
15 cmH20
C.
750 ml
45 cmH20
ml/cmH20
ml/cmH20
If a high compliance is good, which of the above patients [A, B or C] has the best compliance?
Another use of these types of formula by the RCP is the comparison of the patient’s VT in ml to
their ideal body weight in kg [IBW].
RSPT 1325 Sciences: unit 1 lecture/homework page 12
VT/IBW = V` in ml/kg.
VT
A 500 ml
IBW
45 kg
B 750 ml
68 kg
C 675 ml
53 kg
VT in ml/kg.
ml/kg.
ml/kg.
1.
ml/kg.
If you prefer your patient to breathe at 10 ml/kg, which of the above patients: A, B or
C is closest to this ideal?
2.
If your patient must have at least 5 ml/kg of VT to breathe without the help of a
mechanical ventilator, can any of these patients breathe without help?
3.
If your patient IBW is 150 pounds and his VT is 500 ml, how many ml/kg IBW is he
getting. [HINT: must convert pounds to kg]