Respiratory%20Calculations

1
Respiratory Calculations

• Gas Laws
• Oxygen therapy
• Humidity
• Ventilator Management
• Hemodynamics

2
Gas Laws

• Daltons Law
• Ficks Law of Diffusion
• Boyles Law, Charles Law, Gay-Lussacs Combined
  Gas Law
• Grahams Law
• Poiseuilles Law
• Temperature Conversion (C to F and vice versa)

3
Oxygen Therapy

• Total Flow
• Tank Duration
• Arterial Venous O2 Content
• C(a-v)O2 difference
• Alveolar Air Equation
• P(A-a) O2 Gradient
• Heliox flow rates

4
Total Flow
Subtract FiO2 - 20 (or 21)
100
These 2 values Will Determine the Air O2 ratio
FiO2
20 or 21
Subtract 100 - FiO2
If the FiO2 Is .40 or gt Use 20 (lt .40 Use 21)
Add the numbers of the ratio X flow rate Total
flow
5
Total Flow Example
A COPD patient is currently on a 40 aerosol face
mask running at 10 LPM. Calculate the total flow.
20
1
100
40
(1 3) x 10 40 LPM
20
3
60
6
Tank Duration
E cylinder .28 H cylinder 3.14
Pressure of the cylinder
PSIG x Tank factor Flow rate
The flow the O2 Device is set at
7
Tank Duration Example
A patient is currently on a 4 L nasal cannula.
The patient needs to be transported using an E
cylinder. The E cylinder reads 2200 psig on the
Bourdon gauge. According to hospital policy, the
tank should not be used once the pressure reading
reaches 200 psig. Calculate how long the tank
will last
(2200-200) x .28 4
152.6 minutes 60 min/hr
2.54 Hours
8
Arterial Venous O2 Content
Arterial and venous. O2 content represents the
amount of oxygen that is bound to hemoglobin and
dissolved in the blood. The difference is that
arterial O2 content represents the arterial
system (high O2), and venous O2 content
represents the venous system (low O2).
CxO2 (1.34 x Hgb x SxO2) (PxO2 x .003)
O2 carried/bound to hemoglobin
O2 dissolved in blood plasma
9
Comparison of CaO2 CvO2
Arterial O2 Content
CaO2 (1.34 x Hgb x SaO2) (PaO2 x .003)
Partial Pressure Of arterial O2
A constant
Hemoglobin
Arterial saturation
A constant
Venous O2 Content
CvO2 (1.34 x Hgb x SvO2) (PvO2 x .003)
Partial Pressure Of venous O2
Venous saturation
10
Arterial O2 Content Example
Given the following values, calculate the
CaO2 PaO2 93 mmHg PvO2 47 mmHg SaO2
98 SvO2 77 Hemoglobin 16 g/dL
CaO2 (1.34 x 16 x .98) (93 x .003)
CaO2 21.01 .279 21.29 vol
Normal value for CaO2 is approximately 20 vol
11
Venous O2 Content Example
Given the following values, calculate the
CvO2 PaO2 93 mmHg PvO2 47 mmHg SaO2
98 SvO2 77 Hemoglobin 16 g/dL
CvO2 (1.34 x 16 x .77) (47 x .003)
CvO2 16.51 .141 16.65 vol
Normal CvO2 is approximately 15 vol
12
C(a-v) Difference
The C(a-v) difference represents the difference
between arterial And venous oxygen content. It is
a reflection of oxygen Consumption (oxygen used
by tissues within the body)
Recall the values from the 2 previous
examples CaO2 21.29 vol CvO2 16.65 vol
To determine the C(a-v)O2, simply
subtract CaO2 - CvO2
21.29 - 16.65 4.64 vol
Normal C(a-v)O2 5 vol
13
C(a-v) difference Clinical Info
C(a-v)O2 can be an important clinical indicator.
Recall that The C(a-v)O2 reflects the amount of
oxygen taken from arterial Blood to be used by
body tissues. Refer to the diagram below
O2
O2
Arterial CaO2 20 vol
Venous CvO2 15 vol
Tissues
O2
O2
O2 that is NOT extracted From arterial blood
enters Venous circulation
Arterial blood contains Approx 5 vol of O2
5 vol of O2 Is extracted from Arterial blood
14
C(a-v) Difference cont
When blood flows through the body at a normal
rate, approximately 5 vol of the O2 present in
arterial blood is extracted by the tissues. The
remaining O2 enters the venous system. When
blood flows through the body slower than normal,
blood begins To pool and more O2 is taken from
arterial blood. With the tissues Extracting more
O2, less O2 is present in the venous system. If
you Have a lower venous O2 content, and subtract
it from the CaO2, you Get a greater C(a-v)O2
difference
An increase in the C(a-v)O2 difference a
decrease in cardiac output
15
Alveolar Air Equation
The Alveolar air equation represents the
partial Pressure of oxygen in the alveoli
A/C M E M B R A N E
This is what we Are finding using The
alveolar Air equation
Alveolus
PAO2
O2
O2
O2
O2
diffusion
PaO2
Capillary
O2
O2
O2
O2
16
Alveolar Air Equation Cont
PAO2 (PB-PH2O) FiO2 - PaCO2 / .8
O2 concentration
Barometric pressure Normal is 760 mmHg
Arterial CO2
Water pressure Constant 47 mmHg
Constant Respiratory Quotient CO2 removed/O2
consumed 200 mL/ 250 mL .8
17
Alveolar Air Equation Example
Given the following information, calculate the
PAO2 PB 760 mmHg FiO2 .60 PaCO2 40
mmHg PaO2 88 mmHg Hgb 14 g/dL
377.8 mmHg
PAO2 (760 - 47).60 - 40 / .8

18
P(A-a)O2 Gradient
P(A-a)O2 represents the difference between the
partial pressure Of O2 in the alveoli and the
partial pressure of O2 in the arteries. In other
words, it reflects how much of the available O2
(PAO2) Is actually diffusing into the blood
(PaO2).
In a healthy individual, the P(A-a)O2 should be
very small. In other words, the majority of the
available O2 is diffusing Into the blood (refer
to the diagram on the alveolor air Equation
slide for a better understanding)
If the P(A-a)O2 increases, it signals there is
some problem with the gas diffusion mechanism
(shunting for example).
19
P(A-a)O2 Gradient Example
Using the PAO2 calculated earlier (377.8 mmHg),
calculate The P(A-a)O2 if the PaO2 is 80 mmHg
P(A-a)O2 377.8 - 80
297.8 mmHg
What does this number tell you?
This number indicates that a significant amount
of the available O2 is not diffusing into the
blood, indicating a shunt is present
20
Heliox Flow Rates
Heliox is a mixture of helium and oxygen. Because
helium is less Dense than oxygen, it is used to
carry oxygen past airway Obstructions. Because
heliox is less dense than pure oxygen, It has a
faster flow.
2 different heliox mixtures
Multiply flow Reading by A factor of 1.8 To get
actual flow
Multiply flow Reading by A factor of 1.6 to Get
actual flow
Helium Oxygen 80 20 70
30
21
Heliox Flow Rates Example
A physician orders 8020 heliox to be run at 18
LPM. At what flow rate should the flow meter be
set?
We know that Set Flow rate x 1.8 actual flow of
8020 heliox
We can rearrange this equation to solve for the
set flow rate
Set flow rate Actual flow / 1.8 Set flow rate
18 LPM / 1.8 Set flow rate 10 LPM
In order to have an actual flow of 18 LPM, we
need to set the Flow meter at 10 LPM (If this
were a 7030 mixture, replace 1.8 with 1.6)
22
Humidity

• Body Humidity

23
Body Humidity
Normal body humidity is expressed as 44 mg/L or
47 mmHg
This means that at 98.6 F (37 C) gas is saturated
with 44 mgHg or 44 mg/L of water vapor
Relative Humidity
Humidity Deficit
What is the humidity deficit Of a gas saturated
at 30 mg/L Of water at body temperature?
What is the relative humidity Of a gas saturated
with 30 mg/L Of water at body temperature?
30 mg/L 44 mg/L
44 mg/L - 30 mg/L
14 mg/L
68
24
Ventilator Management

• Compliance (dynamic vs. static)
• Resistance
• I-time, peak flow rate, vt
• IE ratio
• Desired CO2 / VE
• Desired PaO2
• VD/VT
• Minute Ventilation / Alveolar Ventilation

25
Compliance
Graph of Mechanical Breath
Generic Equation
? Volume ? Pressure
Dynamic
Static
26
Dynamic Compliance
Tidal Volume (mL) Peak Pressure - PEEP
Dynamic compliance measures the elasticity of the
lung During air movement. It is a less reliable
indicator of lung Elasticity compared to static
compliance
Note Peak Pressure PIP
27
Static Compliance
Tidal Volume (mL) Plateau Pressure - PEEP
Static compliance measures the elasticity of the
lung When there is no air movement. It is the
best indicator Of the ability to ventilate the
lungs.
Normal static compliance is 60 - 70 mL/cmH2O
Note Plateau pressure PPL Static Pressure
28
Understanding Compliance
mL cmH2O
? Volume ? Pressure
Compliance tells that for every1 cmH2O pressure
the lungs Can hold X mL of air. The more mL of
air that a lung can hold Per cmH2O, the more
compliant the lung.
Patient B 60 mL/cmH2O
Example
Patient A 30 mL/cmH2O
Patient B has more compliant lungs. Patient As
lungs Can only hold 30 mL of air for every cmH2O
of pressure, Whereas patient B can hold 60 mL of
air for every cmH2O.
29
Compliance Example 1
Calculate the static compliance given the
following Information FiO2 .60
Rate 12 bpm Peak
Pressure 38 cmH2O Plateau Pressure 29
cmH2O Vt 600 mL
PEEP 5 cmH2O
Vt PPL - PEEP
600 29 - 5
25 mL/cmH2O
30
Compliance Example 2
Calculate the static compliance given the
following Information FiO2 .60
Rate 12 bpm Peak
Pressure 38 cmH2O Plateau Pressure 29
cmH2O Vt 600 mL
PEEP 5 cmH2O
Vt PIP - PEEP
600 38 - 5
18.18 mL/cmH2O
31
Compliance Clinical Scenario
Mr. J arrived to the ER in acute respiratory
distress. He was Subsequently intubated and
placed on mechanical ventilation In the ICU.
Reviewing Mr. Js ventilator sheet reveals
the Following information
800 a.m.
1200 p.m.
400 a.m.
Plateau Pressure
31 cmH2O
22 cmH2O
27 cmH2O
PEEP
5 cmH2O
5 cmH2O
5 cmH2O
Tidal Volume
600 mL
600 mL
600 mL
What does the information reveal about the
compliance of Mr. Js lungs?
32
Compliance Clinical Scenario
600 mL 22 cmH2O - 5 cmH2O
600 mL 27 cmH2O - 5 cmH2O
600 mL 31 cmH2O - 5 cmH2O
35.29 mL/cmH2O
27.27 mL/cmH2O
23.08 mL/cmH2O
Compliance is decreasing --gt Increasing static
pressure results In a decreased compliance
33
Airway Resistance (Raw)
Airway resistance measures the force that opposes
gas flow Through the airway
Normal airflow
Increased Raw
Normal Raw is 0.6 - 2.4 cmH2O/L/Sec on a
non-intubated Patient, and 5 cmH2O/L/Sec on an
intubated patient
34
Airway Resistance (Raw)
Peak Pressure - Plateau Pressure
Flow
Flow must be in L/sec. If flow is given in
L/min, Divide the flow by 60 seconds before
placing It in the equation
Example Convert 60 L/min to L/sec
60 L/min
1 L/sec
60
35
Airway Resistance Example
Calculate the airway resistance, given the
following FiO2 .60
Rate 12 bpm Peak Pressure 38 cmH2O
Plateau Pressure 29 cmH2O Vt 600 mL
PEEP 5 cmH2O Flow 40
LPM
40 LPM 60
1st convert the flow
.67 L/sec
PIP - PPL Flow
38 - 29 .67
13.43 cmH2O/L/Sec
36
I-time, Peak flow, Vt
The following generic equation can be used to
find I-time, peak flow rate, and tidal volume
Tidal Volume (in L) I-time
Peak Flow(LPM) 60

37
Finding I-time
I-time is the inspiratory portion of a breath. In
other words, It is the amount of time spent on
inspiration
E-time
I-time
To find I-time
1st determine the length of a single breath
2nd Use the IE ratio to determine the length
of the I-time
38
I-Time Example
Calculate the I-time given the following
ventilator parameters Vt 600 cc Rate 12
bmp Peak Flow 60 LPM
IE 12 FiO2 .60
1st determine the length of a single breath
There are 12 breaths in 1 minute and 60 seconds
in 1 minute. Therefore 60 seconds / 12 breaths
1 breath every 5 seconds Therefore, then legnth
of 1 breath is 5 seconds
2nd Use the IE ratio to determine the length of
the I-time
1x 2x 5
1x equals the inspiratory portion of the Breath.
1 x 1.67 1.67 seconds
3x 5
X 5/3 or 1.67
39
Finding Peak Flow
Find the peak flow, given the following VT 750
cc RR 15 IE 12.5
First find the I-time (see the previous slide)
1.14 sec
Tidal Volume (in L) I-time
Peak Flow(LPM) 60

X 60
.750 1.14

45 1.14
(.750)60 1.14X
39.47 LPM
40
Finding Vt
Find the Vt given the following PF 50 LPM, RR
14, IE 12
First, Find the I-time 1.43 sec
Tidal Volume (in L) I-time
Peak Flow(LPM) 60

50 60
X 1.43

60X 71.5
X 1.1917 L or 1191.7 mL
(1.43)50 60X
41
IE Ratio
Determine the IE ratio for a patient on a
ventilator breathing 20 bpm, Vt 600 cc, Peak
flow of 50 LPM.
1st, find the I-time
Tidal Volume (in L) I-time
Peak Flow(LPM) 60

. 6 X

50 60
.72 seconds
2nd, Calculate the total breath time
60 seconds 20
3 seconds
42
IE Ratio
I-time .72 seconds Total breath time 5 seconds
Remember that a total breath is composed of an
inspiratory Time and expiratory time, therefore
Total time - I-time E-time
3 - .72 4.28
Convert to a 1X ratio
I-time E-time
1 3.2
.72 2.28 .72
.72 2.28
43
Achieving correct CO2/Minute ventilation
Current VE x Current PaCO2 Desired
PaCO2
Example The doctor wants to decrease a patients
PaCO2 from 50 mmHg to 35 mmHg.
The doctor wants your advice on a proper
minute ventilation. The current settings
include a rate of 12 and a tidal volume of
500 mL.
Current VE 12 x 500
6000 mL or 6 L
You would need to se the Ventilator with a rate
and tidal Volume that equals 8.57 L. (e.g. rate
of 10, Vt of 857 mL)
6L x 50 35
8.57 L
44
Achieving correct PaO2
Desired PaO2 x FiO2 Current PaO2
Example A patient is currently hypoxic with a
PaO2 Of 60 on an FiO2 of .45. The physician
orders to maintain A PaO2 of at least 80 mmHg and
asks you to adjust the Ventilator accordingly

Increase the FiO2 to .60 to achieve a PaO2 Of 80
mmHg
80 mmHg x .45 60 mmHg
.60
45
VD/Vt
The VD/Vt equation illustrates the of gas that
does not Participate in gas exchange. In other
words, it reflects The of gas that is deadspace.
PaCO2 -PeCO2 PaCO2
Deadspace refers to ventilation in the absence of
perfusion
Alveoli
O2
O2
O2
O2
capillary
Blocked blood flow
46
VD/Vt example
Calculate the VD/Vt given the following PaO2
88 mmHg Vt 550 mL PaCO2 40 mmHg
PeCO2 31 mmHg
To determine the actual volume Of deadspace, just
multiply The deadspace by the given Tidal
volume
PaCO2 -PeCO2 PaCO2
40 - 31 40
.225 x 550
123.75 mL
22.5
Normal deadspace 20 - 40, up to 60 on
ventilator
47
Minute/Alveolar Ventilation
Minute ventilation refers the volume of gas
inhaled during A 1 minute period.
Minute ventilation(VE) Tidal volume x
Respiratory rate
Normal Minute ventilation 5 - 10 LPM
Alveolar ventilation refers the the volume of gas
that actually Participates in gas exchange.
Alveolar ventilation (tidal volume - deadspace)
x RR
1 mL/lb of body weight Or 1/3 of tidal volume
48
Example
Calculate the alveolar minute ventilation for a
150 lb male With a respiratory rate of 18 and
tidal volume of 500 mL
Alveolar ventilation (500 - 150) x 18
6300 mL or 6.3 L
49
Hemodynamics

• Shunt
• Pulmonary vascular resistance
• Systemic vascular resistance
• Mean pressure
• Pulse pressure
• Cardiac output (Fick's equation)
• Stroke Volume
• Cardiac Index