Download 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
450:950
35 : X
12.5: 200
X : 950
1: 35.7
X: 87
The numbers on the outside are multiplied
together, while the numbers on the inside
are multiplied together
450 : 950 = 35 : X
450 (X) = 950 (35)
450 X = 33,250
450
450
X = 73.88
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 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:
1:3
1: 4
1:5
The inspiratory
The expiratory time
time is:
is:
1:3 as 1.5 : x
1.5 seconds
2 seconds
1:5 as x : 6
1(6) = 5 x
6=5x
6/5 = 5/5 x
1.2 seconds = x
X= 3(1.5)
X = 4.5
1:4 as 2: x
X= 4(2)
X= 8 seconds
6 seconds
1:1.5
4.5 seconds
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
Another way we use proportions is to calculate drug
dosages.
You solve these:
If the ratio is:
1 mg: 2.5 ml
When You have:
3 mg
Then you would
have:
7.5
ml
1 mg: 2.5 ml as 3 mg : x
1(x) = 2.5 (3)
x = 7.5
2.5 mg : 3 ml
5 mg
6
2.5 mg : 3 ml as 5 mg: x
2.5 x = 3 (5)
ml
2.5 x = 3 (5)
2.5
2.5
X=6
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
25
6 grams: 300 ml as .5 gram : x
6x = 300 (.5)
6 x = 150
6 x = 150
6
6
X = 25
.5 mg: 3 ml
1
.5 mg: 3 ml as 1 mg :x
.5 x = 3 (1)
.5 x = 3
.5 x = 3
.5
.5
X=6
mg.
6 ml
ml
Another example of using ratio is to compare the VD/VT
ratio.
When the VD/VT ratio
is:
1:4
The VD is:
The VT is:
450
1800
200
500
1:4 as 450: x
1x = (4) 450
X = 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
1:3
600
200
1:3 as 200: x
1(x) = (3) 200
x = 600
Still another way that respiratory therapists use ratios is to determine
how much extra oxygen we need to give a patient.
Patient
Pa02
55 torr
Current
Fi02:
.45
We want Pa02:
We need Fi02 of:
85 torr
.695
.35
64
.5o
55: .45 as 85 : x
55 x = .45(85)
55 x = 38.25
55 x = 38.25
55
55
X = .6954
45 torr
45: .35 as x : .5
45 (.5) = .35x
22.5 = 35 x
22.5 = 35 x
35
35
.642 = x
45 torr
.28
65 torr
.40
.21
160
.45
45: .28 as 65: x
45x = .28 (65)
45x = 18.2
45x = 18.2
45
45
X = .4044
75 torr
75: .21 as x : .45
75(.45) = .21 x
33.75 = .21 x
33.75 = .21 x
.21
.21
X = 160
1.
[pp. 36-41] Be able to calculate proportions.
a. Directly proportional relationships result in
numbers that increase or decrease as their related
numbers increase or decrease.
V
T
V
=k
1800
T
40
K [Pressure]
45
900
20
45
100
2.22
45
200
4.44
45
V/T = k
x/40 = 45
40 (x/40) = 45 (40)
X = 1800
V/T = k
x/20 = 45
20 (x/20) = 45 20)
X = 900
V/T = k
100/x = 45
x (100/x) = 45 x
100 = 45 x
100 = 45 x
45
45
2.222 = x
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
b. Inverse proportional relationships 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
P (15) =20
15
15
P = 1.33
Do these:
V
30
k [temperature]
35
45
35
.777
60
35
.58
90
35
.388
Based on the above table, discuss the relationship between the V & the P
when the temperature is constant.


2.
P
1.166
When the V drops, the P rises
When the V rises, the P drops
[pp 59-64] Be able to perform dimensional analysis.
a. When the respiratory therapist has to compare items with different
units, we must use dimensional analysis.
b. 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:
20 cmH20
In mmHg, this would be
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:
A. 100 ml
And a P:
25 cmH20
Calculate the C:
100/25=4
4 ml/cmH20
B.
300 ml
15 cmH20
C.
750 ml
45 cmH20
300/15= 20
20 ml/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?

3.
B is closest to 10 ml/kg
[pp. 4-12] be able to calculate problems with
scientific notation and exponents.
a. 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.
b. 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:
100
10
102
100
104
10,000
105
100,000
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
10-1
10-3
10-5
10-6
As a fraction
1/10
.1
1/1000
.001
1/100,000 correction
.00001
1/1,000,000
.000001
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?
1
101
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 have to 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:
2
8
1010
10
10
1022
1020
102
106
103
103
1030
105
1025
When exponents are divided we would subtract the exponents
1025
= 10 25-2 = 10 23
102
Exponent
Divided by:
Equals:
106
108
102
1018
1020
102
100
103
103
1034
1059
1025
4.
[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
-125
add
100
equals
-25
-250
-18
15
22
-235
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
-125
-250
-18
add
-100
-15
-22
equals
-225
-265
-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.
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i15/bk7_15i1.htm
Subtracting a negative number is just like adding a positive number:
1 – (-3) = 1 + 3
&
-3 – (-8) = -3 + 8
EXAMPLES:
subtraction Convert to addition
3–9=
3+-9
-2 - 9
-2 + 9
-150-125
-150 + 125
equals
-6
7
-25
You do these:
subtraction
31 - 19
-12 - 8
-15 -1
Convert to addition
31 + (-19)
-12 + (-8)
-15 + (-1)
equals
12
- 20
-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.
5.
Be able to answer word problems based on the math
skills in Part II