Respiratory Calculations
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Gas Laws
Oxygen therapy
Humidity
Ventilator Management
Hemodynamics
Gas Laws
• Dalton’s Law
• Fick’s Law of Diffusion
• Boyle’s Law, Charles Law, Gay-Lussac’s
Combined Gas Law
• Graham’s Law
• Poiseuille’s Law
• Temperature Conversion (C to F and vice
versa)
Oxygen Therapy
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Total Flow
Tank Duration
Arterial & Venous O2 Content
[C(a-v)O2] difference
Alveolar Air Equation
P(A-a) O2 Gradient
Heliox flow rates
Total Flow
Subtract
FiO2 - 20 (or 21)
100
FiO2
If the FiO2
Is .40 or >
Use 20 (< .40
Use 21)
20 or
21
Subtract
100 - FiO2
These 2 values
Will
Determine the
Air: O2 ratio
Add the numbers of the ratio X flow rate = Total flow
Total Flow: Example
A COPD patient is currently on a 40% aerosol face
mask running at 10 LPM. Calculate the total flow.
20
100
1
40
20
(1 + 3) x 10 = 40 LPM
60
3
Tank Duration
Pressure of the cylinder
E cylinder: .28
H cylinder: 3.14
PSIG x Tank factor
Flow rate
The flow the O2
Device is set at
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
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
Comparison of CaO2 & CvO2
Arterial O2 Content
CaO2 = (1.34 x Hgb x SaO2) + (PaO2 x .003)
A constant
Hemoglobin Arterial Partial
saturation Pressure A constant
Of arterial
O2
Venous O2 Content
CvO2 = (1.34 x Hgb x SvO2) + (PvO2 x .003)
Partial
Venous
Pressure
saturation Of venous
O2
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 %
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 %
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 %
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
Arterial: CaO2 = 20 vol%
Arterial blood contains
Approx 5 vol% of O2
O2
Tissues
O2
O2
5 vol% of O2
Is extracted from
Arterial blood
Venous: CvO2 = 15 vol%
O2 that is NOT extracted
From arterial blood enters
Venous circulation
C(a-v) Difference con’t…
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
Alveolar Air Equation
The Alveolar air equation represents the partial
Pressure of oxygen in the alveoli
A/C
This is what we
Are finding using
The alveolar
Air equation
Alveolus
PAO2
O2
O2
O2 O2
diffusion
PaO2
O2
O2
O2
O2
Capillary
M
E
M
B
R
A
N
E
Alveolar Air Equation: Con’t…
PAO2 = [(PB-PH2O) FiO2] - PaCO2 / .8
Barometric pressure
Normal is 760 mmHg
O2 concentration
Water pressure
Constant:
47 mmHg
Arterial
CO2
Constant: Respiratory
Quotient
CO2 removed/O2 consumed
200 mL/ 250 mL
= .8
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
PAO2 = [(760 - 47).60] - 40 / .8 = 377.8 mmHg
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).
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
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
Helium : Oxygen
80
: 20
70
: 30
Multiply flow
Reading by
A factor of 1.6 to
Get actual flow
Heliox Flow Rates: Example
A physician orders 80:20 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 80:20 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 70:30 mixture, replace
1.8 with 1.6)
Humidity
• Body Humidity
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:
What is the relative humidity
Of a gas saturated with 30 mg/L
Of water at body temperature?
30 mg/L
44 mg/L
= 68%
Humidity Deficit:
What is the humidity deficit
Of a gas saturated at 30 mg/L
Of water at body temperature?
44 mg/L - 30 mg/L = 14 mg/L
Ventilator Management
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Compliance (dynamic vs. static)
Resistance
I-time, peak flow rate, vt
I:E ratio
Desired CO2 / VE
Desired PaO2
VD/VT
Minute Ventilation / Alveolar Ventilation
Compliance
Generic Equation
Graph of Mechanical Breath
∆ Volume
∆ Pressure
PIP (dynamic pressure)
Pressure
Or
volume
P lateau pressure
Insp. Hold
Dynamic
Static
PEEP
change-over from
insp to exp
I-T ime
NEEP
E-Time
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
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
Understanding Compliance
∆ Volume
∆ Pressure
mL
cmH2O
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.
Example:
Patient A:
30 mL/cmH2O
Patient B:
60 mL/cmH2O
Patient B has more compliant lungs. Patient A’s 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.
Compliance Example 1
Calculate the static compliance given the following
Information:
FiO2: .60
Peak Pressure: 38 cmH2O
Vt: 600 mL
Vt
PPL - PEEP
600
29 - 5
Rate: 12 bpm
Plateau Pressure: 29 cmH2O
PEEP: +5 cmH2O
25 mL/cmH2O
Compliance Example 2
Calculate the static compliance given the following
Information:
FiO2: .60
Peak Pressure: 38 cmH2O
Vt: 600 mL
Vt
PIP - PEEP
600
38 - 5
Rate: 12 bpm
Plateau Pressure: 29 cmH2O
PEEP: +5 cmH2O
18.18 mL/cmH2O
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. J’s ventilator sheet reveals the
Following information:
8:00 a.m.
Plateau Pressure: 22 cmH2O
PEEP:
5 cmH2O
Tidal Volume:
600 mL
12:00 p.m.
27 cmH2O
5 cmH2O
600 mL
4:00 a.m.
31 cmH2O
5 cmH2O
600 mL
What does the information reveal about the compliance of
Mr. J’s lungs?
Compliance Clinical Scenario
600 mL
600 mL
600 mL
22 cmH2O - 5 cmH2O 27 cmH2O - 5 cmH2O 31 cmH2O - 5 cmH2O
35.29 mL/cmH2O
27.27 mL/cmH2O
23.08 mL/cmH2O
Compliance is decreasing --> Increasing static pressure results
In a decreased compliance
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
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
60
1 L/sec
Airway Resistance Example
Calculate the airway resistance, given the following
FiO2: .60
Peak Pressure: 38 cmH2O
Vt: 600 mL
Flow: 40 LPM
40 LPM
60
1st convert the flow
PIP - PPL
Flow
Rate: 12 bpm
Plateau Pressure: 29 cmH2O
PEEP: +5 cmH2O
38 - 29
.67
.67 L/sec
13.43 cmH2O/L/Sec
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
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 I:E ratio to determine the length
of the I-time
I-Time Example
Calculate the I-time given the following ventilator parameters
Vt: 600 cc
Rate: 12 bmp
Peak Flow: 60 LPM
I:E = 1:2
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 I:E ratio to determine the length of the I-time
1x + 2x = 5
1x equals the inspiratory portion of the
3x = 5
Breath. 1 x 1.67 = 1.67 seconds
X = 5/3 or 1.67
Finding Peak Flow
Find the peak flow, given the following
VT = 750 cc
RR = 15
I:E = 1:2.5
First find the I-time (see the previous slide): 1.14 sec
Tidal Volume (in L) = Peak Flow(LPM)
I-time
60
.750
1.14
(.750)60 = 1.14X
X
60
=
45
1.14
39.47 LPM
Finding Vt
Find the Vt given the following:
PF = 50 LPM, RR = 14, I:E = 1:2
First, Find the I-time: 1.43 sec
Tidal Volume (in L) = Peak Flow(LPM)
I-time
60
X
1.43
(1.43)50 = 60X
=
60X
71.5
50
60
X = 1.1917 L or
1191.7 mL
I:E Ratio
Determine the I:E 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) = Peak Flow(LPM)
I-time
60
. 6 = 50
.72 seconds
X
60
2nd, Calculate the total breath time:
60 seconds
20
3 seconds
I:E 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
I-time : E-time
.72 : 2.28
Convert to a 1:X ratio
.72 : 2.28
.72
1 : 3.2
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
6L x 50
35
8.57 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)
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
80 mmHg x .45
60 mmHg
Increase the FiO2 to
.60 .60 to achieve a PaO2
Of 80 mmHg
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
O2
O2
O2
O2
Alveoli
capillary
Blocked blood flow
VD/Vt example
Calculate the VD/Vt given the following:
PaO2: 88 mmHg
PaCO2: 40 mmHg
PaCO2 -PeCO2
PaCO2
40 - 31
40
Vt: 550 mL
PeCO2: 31 mmHg
To determine the actual volume
Of deadspace, just multiply
The % deadspace by the given
Tidal volume:
.225 x 550 = 123.75 mL
= 22.5%
Normal deadspace: 20 - 40%, up to 60% on ventilator
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
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
Hemodynamics
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Shunt
Pulmonary vascular resistance
Systemic vascular resistance
Mean pressure
Pulse pressure
Cardiac output (Fick's equation)
Stroke Volume
Cardiac Index