RSPT 1325 Respiratory Care Sciences

RSPT 1325 Respiratory Care Sciences

Lecture by Elizabeth Kelley Buzbee A.A.S., R.R.T.-N.P.S.,R.C.P.

Part II: Intermediate math KEY

[pp. 33-36] Be able to calculate proportions.

Ratio A / Ratio B / The numbers on the outside are multiplied together, while the numbers on the inside are multiplied together
450:950 / 35 : X / 450 : 950 = 35 : X
450 (X) = 950 (35)
450 X = 33,250
450 450
X = 73.88
12.5: 200 / X : 950 / 12.5: 200 as X :950
12.5 (950) = 200 X
11,875 = 200 x
11,875 = 200 x
200 200
59.375 = X
1: 35.7 / X: 87 / 1: 35.7 as X: 87
(1) 87 = 35.7 x
87= 35.7 x
87 = 35.7 x
35.7 35.7
X= 2.436

In respiratory care the therapist may have to figure out an inspiratory time with a known inspiratory: expiratory ratio [I:E].

You solve these:

If the I:E ratio is: / The inspiratory time is: / The expiratory time is:
1:3 / 1.5 seconds / 1:3 as 1.5 : x
X= 3(1.5)
X = 4.5
1: 4 / 2 seconds / 1:4 as 2: x
X= 4(2)
X= 8 seconds
1:5 / 1:5 as x : 6
1(6) = 5 x
6 = 5 x
6/5 = 5/5 x
1.2 seconds = x / 6 seconds
1:1.5 / 1: 1.5 as x : 4.5
1(4.5) = 1.5 x
4.5 / 1.5 = 1.5/1.5 x
3 seconds = x / 4.5 seconds

Another way we use proportions is to calculate drug dosages.

You solve these:

If the ratio is: / When You have: / Then you would have:
1 mg: 2.5 ml / 3 mg
1 mg: 2.5 ml as 3 mg : x
1(x) = 2.5 (3)
x = 7.5 / 7.5 ml
2.5 mg : 3 ml / 5 mg
2.5 mg : 3 ml as 5 mg: x
2.5 x = 3 (5)
2.5 x = 3 (5)
2.5 2.5
X = 6 / 6 ml
45 grams: 150 ml / 900 grams / 3000 ml
45 grams: 150 ml as x : 3000 ml
45 (3000) = 150 x
135,000 = 150 x
135,000 = 150 x
150 150
X = 900
6 grams: 300 ml / .5 grams
6 grams: 300 ml as .5 gram : x
6x = 300 (.5)
6 x = 150
6 x = 150
6 6
X = 25 / 25 ml
.5 mg: 3 ml / 1 mg.
.5 mg: 3 ml as 1 mg :x
.5 x = 3 (1)
.5 x = 3
.5 x = 3
.5 .5
X = 6 / 6 ml

Another example of using ratio is to compare the VD/VT ratio.

When the VD/VT ratio is: / The VD is: / The VT is:
1:4
1:4 as 450: x
1x = (4) 450
X = 1800 / 450 / 1800
1:2.5
1:2.5 as x : 500
1(500) = 2.5 x
500 = 2.5 x
2.5 2.5
200 = x / 200 / 500
1:3
1:3 as 200: x
1(x) = (3) 200
x = 600 / 200 / 600

Still another way that respiratory therapists use ratios is to determine how much extra oxygen we need to give a patient.

Patient Pa02 / Current Fi02: / We want Pa02: / We need Fi02 of:
55 torr
55: .45 as 85 : x
55 x = .45(85)
55 x = 38.25
55 x = 38.25
55 55
X = .6954 / .45 / 85 torr / .695
45 torr
45: .35 as x : .5
45 (.5) = .35x
22.5 = 35 x
22.5 = 35 x
35 35
.642 = x / .35 / 64 / .5o
45 torr
45: .28 as 65: x
45x = .28 (65)
45x = 18.2
45x = 18.2
45 45
X = .4044 / .28 / 65 torr / .40
75 torr
75: .21 as x : .45
75(.45) = .21 x
33.75 = .21 x
33.75 = .21 x
.21 .21
X = 160 / .21 / 160 / .45

[pp. 36-41] Be able to calculate proportions.
Directly proportionalrelationships result in numbers that increase or decrease as their related numbers increase or decrease.

V = k

V / T / K [Pressure]
1800
V/T = k
x/40 = 45
40 (x/40) = 45 (40)
X = 1800 / 40 / 45
900
V/T = k
x/20 = 45
20 (x/20) = 45 20)
X = 900 / 20 / 45
100
V/T = k
100/x = 45
x (100/x) = 45 x
100 = 45 x
100 = 45 x
45 45
2.222 = x / 2.22 / 45
200 / 4.44 / 45

Based on the above table, discuss the relationship between the V and the T when the P stays the same.

As the V drops the T drops
As the V rise the T rises

Inverse proportionalrelationships result in numbers that decrease as the other number increases, or increases as the other number decreases.

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

15 15

P =1.33

Do these:

V / P / k [temperature]
30 / 1.166 / 35
.777 / 45 / 35
60 / .58 / 35
.388 / 90 / 35

Based on the above table, discuss the relationship between the V & the P when the temperature is constant.

When the V drops, the P rises
When the V rises, the P drops

[pp 59-64] 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.

EXAMPLE: You have a patient who weighs 150 pounds; you need to know how many kg he weighs.

The conversion from pounds to kg is pounds /2.2 = kg

You do these:

Your patient weighs: / His weight in kg:
235 pounds / 106.8
15 pounds / 6.8
185 pounds / 84
5 pounds / 2.27

The conversion between these two units of pressure is 1.46 mmHg /1 cmH20.
the conversion from mmHg to cmH20 is .735cmH20/1 mmHg.

You do these:

Your airway pressure is: / In mmHg, this would be
20 cmH20 / 27.21
15 cmH20 / 20.4
30.8 / 45 mmHg
24.48 / 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 smaller volume into the lungs

C= VT/P

C= 50 ml/10 cmH20

C= 5 ml/cmH20

Do these:

If you have VT: / And a P: / Calculate the C:
A. 100 ml / 25 cmH20 / 100/25=4
4 ml/cmH20
B. 300 ml / 15 cmH20 / 300/15= 20
20 ml/cmH20
C. 750 ml / 45 cmH20 / 750/45= 16.66
16.66 ml/cmH20

If a high compliance is good, which of the above patients [A, B or C] has the best compliance?

B has the highest compliance

Another use of these types of formula by the RCP is the comparison of the patient VT in ml to their ideal body weight in kg [IBW].

VT/IBW = Vt in ml/kg.

VT / IBW / Vt in ml/kg.
A 500 ml / 45 kg / 500/ 45= 11.1 ml/kg.
B 750 ml / 68 kg / 750/68= 11.02 ml/kg.
C 675 ml / 53 kg / 675/53= 12.73 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?

B is closest to 10 ml/kg

[pp. 4-12] be able to calculate problems with scientific notation and exponents.
In medicine, we work with extremely large or extremely small figures. To make it easer to understand and to work with these figures, sometimes we have to use scientific notation and exponents.
For example: Instead of writing 1000, we could write this same number as 103 which is a short cut for 10 x 10 x 10.

The number: / As an exponent:
10 / 100
100 / 102
10,000 / 104
100,000 / 105

When we change a number to an exponent we are telling ourselves to move the decimal a certain number of spaces to the left to discuss large numbers.

The exponent: / We would move the decimal how many spaces to the left?
101 / 1
102 / 2
103 / 3
1030 / 30

We can also use exponents to discuss really small numbers such as .00001 which would be referred to as 10-5

a number less than 1 is also a fraction. .01 is 10-2 and it is also the fraction 1/100

The number / As an exponent / As a fraction
.1 / 10-1 / 1/10
.001 / 10-3 / 1/1000
.00001 / 10-5 / 1/100,000correction
.000001 / 10-6 / 1/1,000,000

In this case, we are moving the decimal a certain number of spaces to the right to discuss tiny numbers.

The exponent / We would move the decimal how many spaces to the right?
10-1 / 1
10-2 / 2
10-3 / 3
10-30 / 30

IF you had a huge number such as 230,000 you could call it 2.3 x 105

NOTE:When using exponents, we haveto reduce the number to a number between 1 and 10 so 230,000 is not 23 x 104

The number / As an exponent
.5 / 5 x 10-1
5000 / 5 x 103
.007 / 7 x 10-3
700 / 7x 102
.00008 / 8 x 10-5
880,000 / 8.8 x 106
.000009 / 9 x 10-6

Multiplying or dividing exponents

When multiplying numbers with exponents we would add the exponents:

105 ( 103) = 10 5 +3 = 108

Exponent / Multiplied by: / Equals:
102 / 108 / 1010
1020 / 102 / 1022
103 / 103 / 106
105 / 1025 / 1030

When exponents are divided we would subtract the exponents

1025

102 = 10 25-2 = 10 23

Exponent / Divided by: / Equals:
108 / 102 / 106
1020 / 102 / 1018
103 / 103 / 100
1059 / 1025 / 1034

[pp. 136-138]Work with negative and positive numbers.

Respiratory therapists must understand pressure and vacuum.

A negative number is one that is less than 0
A positive number is one that is more than 0 [the origin]
If you have a pressure that is 3 cmH20 below zero, we would call this -3 cmH20.

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

If you have a pressure that is 14 mmHg above zero, it is called 14 mmHg.

Addition of negative and positive numbers:

If a negative number is added to a positive number, the resulting number will move toward the zero.

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

-2 + 2 = 0

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

-6 + 2= -4

You do these:

number / add / equals
-125 / 100 / -25
-250 / 15 / -235
-18 / 22 / 4

Addition of two negative numbers: would move away from the zero:

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

-2 + -2 = -4

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

-2 + -5 = -7

You do these:

number / add / equals
-125 / -100 / -225
-250 / -15 / -265
-18 / -22 / -40

subtraction of negative and positive numbers

If a negative number is subtracted from a positive number, we need to convert the formula to addition then follow those rules

If both numbers are negative, it's just like adding positive numbers, except that the answer is negative.

Subtracting a negative number is just like adding a positive number:

1 –(-3) = 1 + 3

-3 –(-8) =-3 + 8

EXAMPLES:

subtraction / Convert to addition / equals
3 – 9 = / 3 + -9 / -6
-2 - 9 / -2 + 9 / 7
-150-125 / -150 + 125 / -25

You do these:

subtraction / Convert to addition / equals
31 - 19 / 31 + (-19) / 12
-12 - 8 / -12 + (-8) / - 20
-15 -1 / -15 + (-1) / -16

Situations in which the RCP might subtract positive and negative numbers:

As a person breathes in his chest creates negative pressure because as his chest wall volume increases, the pressure inside the chest decreases [remember Boyle’s Law]

If the pressure at the mouth is considered zero, and the airway pressure is zero, once the volume rises and the pressure drops to -5 cmH20, we would have 0- -5 cmH20 = 0 + (-5) = 5 cmH20 of driving pressure. Air moves into this vacuum.

Be able to answer word problems based on the math skills in Part II