Lawrence Martin, M.D.
Clinical Professor of Medicine
Case Western Reserve University School of Medicine
Cleveland, OHIO USA
larry.martin@roadrunner.com
September 17, 2009
Because your understanding the PaCO2
equation will:
Save lives!
Improve patient care!
Help wean patients off the ventilator!
Shorten length of stay!
PaCO2 Equation: PaCO2 reflects ratio of
metabolic CO2 production (VCO2) to
alveolar ventilation (VA)
PaCO2 =
VCO2 x 0.863
------------------VA
VCO2 = CO2 production
VA = VE – VD
VE = minute (total) ventilation = f (tidal volume)
VD = dead space ventilation = f (dead space volume)
0.863 converts VCO2 and VA units to mm Hg
PaCO2
Condition
in blood
State of
alveolar ventilation
> 45 mm Hg
Hypercapnia
Hypoventilation
35 - 45 mm Hg
Eucapnia
Normal ventilation
< 35 mm Hg
Hypocapnia
Hyperventilation
PaCO2 Equation: PaCO2 reflects ratio of metabolic
CO2 production (VCO2) to alveolar ventilation (VA)
PaCO2 =
VCO2 x 0.863
------------------VA
VCO2 = CO2 production
VA = VE – VD
VE = minute (total) ventilation = f (tidal volume)
VD = dead space ventilation = f (dead space volume)
0.863 converts VCO2 and VA units to mm Hg
Normal Resting
VCO2 = 200 ml/minute
f(tidal volume) = 12 (500 ml) = 6 l/min
f(dead space vol.) = 12 (150 ml) = 1.80 l/min
VA = 6 – 1.80 = 4.2 l/min
200 x 0.863
PaCO2 = ----------------4.2
= 41 mm Hg
PaCO2 Equation: PaCO2 reflects ratio of metabolic
CO2 production (VCO2) to alveolar ventilation (VA)
PaCO2 =
VCO2 x 0.863
------------------VA
VCO2 = CO2 production
VA = VE – VD
VE = minute (total) ventilation = f (tidal volume)
VD = dead space ventilation = f (dead space volume)
0.863 converts VCO2 and VA units to mm Hg
Rapid Breathing, normal tidal volume
VCO2 = 200 ml/minute
f(tidal volume) = 24 (500 ml) = 12 l/min
f(dead space vol.) = 24 (150 ml) = 3.60 l/min
VA = 12 – 3.60 = 8.4 l/min
200 x 0.863
PaCO2 = ----------------8.4
= 20.5 mm Hg
PaCO2 Equation: PaCO2 reflects ratio of metabolic
CO2 production (VOC2) to alveolar ventilation (VA)
PaCO2 =
VCO2 x 0.863
------------------VA
VCO2 = CO2 production
VA = VE – VD
VE = minute (total) ventilation = f (tidal volume)
VD = dead space ventilation = f (dead space volume)
0.863 converts VCO2 and VA units to mm Hg
Rapid Breathing, Shallow Tidal Volume
VCO2 = 200 ml/minute
f(tidal volume) = 20 (300 ml) = 6 l/min
f(dead space vol.) = 20 (150 ml) = 3.00 l/min
VA = 6 – 3 = 3 l/min
200 x 0.863
PaCO2 = ----------------3
= 57.5 mm Hg
PaCO2 Equation: PaCO2 reflects ratio of metabolic
CO2 production (VCO2) to alveolar ventilation (VA)
PaCO2 =
VCO2 x 0.863
------------------VA
VCO2 = CO2 production
VA = VE – VD
VE = minute (total) ventilation = f (tidal volume)
VD = dead space ventilation = f (dead space volume)
0.863 converts VCO2 and VA units to mm Hg
Rapid breathing, increased dead space (severe COPD)
VCO2 = 200 ml/minute
f(tidal volume) = 16 (500 ml) = 8 l/min
f(dead space vol.) = 16 (300 ml) = 4.80 l/min
VA = 8 – 4.8 = 3.2 l/min
200 x 0.863
PaCO2 = ----------------- = 54 mm Hg
3.2
PaCO2 is the center of the blood gas universe; without
understanding PaCO2 you can’t understand oxygenation
or acid-base balance.
Oxygenation
Acid-Base
PAO2 = FIO2 (BP-47) – 1.2 (PCO2)
HCO3
pH ~ -----------PaCO2
PaO2



PaCO2 =
VCO2 x .863
-------------------VA
where VA = VE - VD
Note: PaCO2 is from ABGs. HCO3 is calculated from ABG measurement of pH and PaCO2
or measured in venous blood as part of electrolytes. When measured in venous
blood it is variously labeled ‘bicarbonate’, ‘HCO3’ or ‘CO2’ (the latter NOT to be
confused with PaCO2).
Arterial blood – blood gases
Venous blood - BMP
PaCO2 is the center of the blood gas universe.
.
pH
PaO2
PaCO2
HCO3
SaO2
You can’t learn this material from a
lecture!!
Review:
www.lakesidepress.com/pulmonary/index-phys.html
index to web sites on pulmonary physiology
www.lakesidepress.com/ABGQuiz2009-Questions.htm
multiple-choice blood gas quiz
www.lakesidepress.com/pulmonary/papers/eq/tablecontents.html
4 Most Important Equations in Clinical Practice
www.lakesidepress.com/pulmonary/ABG/MixedAB.htm
Diagnosing mixed acid-base disorders
www.lakesidepress.com/pulmonary/ABG/PO2.htm
PaO2, SaO2 & CaO2 – What’s the Difference?
Hypercapnia – PaCO2 > 45 mm Hg
PaCO2
VCO2 x 0.863
=
-----------------VA
where VA = VE – VD
Hypercapnia is a serious respiratory problem. The PaCO2 equation
shows that the only physiologic reason for elevated PaCO2 is inadequate
alveolar ventilation (VA) for the amount of metabolic CO2 production
(VCO2).
Since alveolar ventilation (VA) equals minute ventilation (VE) minus
dead space ventilation (VD), hypercapnia can arise from insufficient VE,
increased VD, or a combination of both.
Hypercapnia (cont)
PaCO2 =
VCO2 x 0.863
-----------------VA
where VA = VE – VD
VA = f(tidal vol.) –
f(dead space vol.)
Examples of inadequate VE leading to decreased VA and
hypercapnia: sedative drug overdose; respiratory muscle
paralysis; central hypoventilation
Examples of increased VD leading to decreased VA and
hypercapnia: chronic obstructive pulmonary disease; severe
restrictive lung disease (with shallow, rapid breathing)
Dangers of Hypercapnia
Besides indicating a serious derangement in the respiratory system,
elevated PaCO2 poses a threat for three reasons:
An elevated PaCO2 will lower the PAO2 (see Alveolar gas equation)
and as a result will lower the PaO2.
2) An elevated PaCO2 will lower the pH (see Henderson-Hasselbalch
equation) and as result lead to acidosis.
3) The higher the baseline PaCO2, the more it will rise for a given fall in
alveolar ventilation, e.g., a given decrease in VA will raise the PaCO2 more
when PaCO2 is 50 mm Hg than when it is 40 mm Hg.
1)
Dangers of Hypercapnia – lowers PAO2 & PaO2
An elevated PaCO2 will lower the PAO2 and as a result will lower the PaO2
Alveolar Gas Equation determines the alveolar PO2 (PAO2).
PAO2 is one of two main factors that determine PaO2.
(The other is ventilation-perfusion relationships within in
the lungs.)
PAO2 = FIO2 (BP-47) – 1.2 (PaCO2)
PaO2
Dangers of Hypercapnia – lowers PAO2 & PaO2
An elevated PaCO2 will lower the PAO2 and as a result will lower the PaO2
PAO2 = FIO2 (BP-47) – 1.2 (PaCO2)
=.21 (760-47) – 1.2 (40)
= 150 – 48 = 102
PAO2 = FIO2 (BP-47) – 1.2 (PaCO2)
=.21 (760-47) – 1.2 (60)
= 150 – 72 = 78
Assuming 10 mm (A-a) O2 difference,
PaO2 = 92 mm Hg
Assuming 10 mm (A-a) O2 difference,
PaO2 = 68 mm Hg
Dangers of Hypercapnia – lowers the pH
An elevated PaCO2 will lower the pH, as predicted by
the Henderson-Hasselbalch Equation.
HCO3
pH ~ -----------PaCO2
Dangers of Hypercapnia – lowers the pH
An elevated PaCO2 will lower the pH, as predicted by
the Henderson-Hasselbalch Equation.
HCO3
pH ~ -----------PaCO2
Normal
24 mEq/l
7.40 ~ -----------40 mm Hg
Respiratory Acidosis
24 mEq/l
7.23 ~ -----------60 mm Hg
Basic Metabolic Panel from venous blood (BMP)
Na+
K+
Cl
HCO3
BUN
Creatinine
140
4.0
95
35
20
1.1
mEq/L
mEq/L
mEq/L
mEq/L
mg%
mg%
HCO3 and PaCO2 are 2 of 3 components in
HCO3
the H-H equation:
pH ~ -----------PaCO2
What does HCO3 by itself reveal about
PaCO2?
Any venous HCO3 can
reflect virtually any
value of PaCO2.
Shown here is venous
HCO3 of 35 mEq/L ,
plotted on graph of H-H
equation.
The range of
possible PaCO2
values is below 20 to
above 100.
Abbreviated H-H equation:
HCO3
pH ~ -----------PaCO2
Knowing just one parameter doesn’t tell
you the acid-base state; you need at least
two of the three values in H-H equation!
Dangers of Hypercapnia –
less reserve if there is
further hypoventilation
Effect of 1 liter decreases
in alveolar ventilation
on PaCO2, when
VCO2 = 200 ml/min
VCO2 x 0.863
PaCO2 = --------------VA
A one-liter decrease in VA when
PaCO2 is 40 mm Hg will increase
PaCO2 to 52 mm Hg.
The next one-liter decrease in VA will
increase PaCO2 to 75 mm Hg…
And the next 1 liter decrease in VA
will increase PaCO2 to 133 mm
Hg!
PaCO2
High PaCO2 increases the slope of
change for any further decrease in
VA
High PaCO2 is dangerous!
VA (l/min)
Dangers of Hypercapnia – summary
PaCO2 of 60 mm Hg is not ‘just 50% higher’
than 40mm Hg. A high PaCO2 also:
Lowers PaO2 at any given Bar. Press.
PAO2 = PIO2 – 1.2(PaCO2)
PAO2 > PaO2

Makes patient acidotic
pH ~ HCO3
PaCO2

Increases the slope of change for any
further decrease in VA.
VCO2 x 0.863
PaCO2 = ------------VA
For VCO2 of 200 and 300
ml/min
PaCO2

Graph of:
VA (l/min)
You cannot assess PaCO2 clinically – Why not?
50-year-old man with COPD:
 respiratory rate 35/minute;
agitated
BP 170/104 mm Hg
Pulse 105/minute
Good breath sounds
Is he hyperventilating?
Hypoventilating? No way
to tell clinically.
At bedside can’t determine
if PaCO2 high or low
because:
VCO2 x 0.863
PaCO2 = -----------------------VA
= f(tidal vol. –
f(dead space vol.)
You don’t know:
- VCO2
- tidal volume
- dead space
volume
Trying to assess PaCO2 clinically can lead to fatal or near fatal errors!
Case – 73 yo woman in hospital
(continued)
 Intern called to bedside at 11 pm
because “she is agitated.” She was
previously calm all day.
Check of her lab work shows that 2 days
earlier, on hospital admission, her
venous HCO3 was 35 mEq/L
(normal up to 29).
 Respiratory rate 20 (mild
tachypnea). Lungs clear. Intern
assess “hypreventilation” and
prescribes Valium to “calm her
down.”
 45 minutes later patient stops
breathing, is emergently intubated.
(continued)
ERROR
Intern didn’t think of hypoventilation in setting of
agitation.
VCO2
PaCO2 =--------VA = f(tidal vol.) – f(dead space vol.)
The only parameter known to intern was
frequency of breathing (fast). Knowing just ‘f’,
it is impossible to reliably gauge if patient is
hyperventilating or hypoventilating. High
HCO3 (not noted by intern) was certainly
consistent with latter. Without check of ABG,
Valium should not have been given!
Hyperventilating? Hypoventilating?
Cannot reliably assess PaCO2 clinically
PaCO2 is
determined only by factors
in the PaCO2 equation:
VCO2 x 0.863
PaCO2 = -------------------VA = f(tidal vol. –
f(dead space vol.)
VCO2 = metabolic CO2 production/min
VA = alveolar ventilation
f = frequency of breathing
0.863 converts units to mm Hg
 The ONLY clinical parameter in
PaCO2 equation is frequency of
breathing!!!
 There is nothing in PaCO2
equation about respiratory
effort, mental status, body
habitus, etc.
 If all you know at bedside is
resp. rate, you can’t possibly
discern patient’s PaCO2!!
 You cannot determine at
bedside if patient’s PaCO2
is high or low.
PaCO2 is key to the blood gas universe; without understanding
PaCO2 you can’t understand oxygenation or acid-base.
Oxygenation
PAO2 = FIO2 (BP-47) – 1.2 (PCO2)
Acid-Base
HCO3
pH ~ -----------PaCO2
PaO2




PaCO2 =
VCO2 x .863
-------------------VA
where VA = VE = VD
= f(VT) – f(VD)
PaCO2 and Alveolar Ventilation: Test Your
Understanding
1. What is the PaCO2 of a patient with respiratory rate 24/min,
tidal volume 300 ml, dead space volume 150 ml, CO2
production 300 ml/min? The patient shows some evidence
of respiratory distress.
.
PaCO2 and Alveolar Ventilation: Test Your
Understanding
1. What is the PaCO2 of a patient with respiratory rate 24/min,
tidal volume 300 ml, dead space volume 150 ml, CO2
production 300 ml/min? The patient shows some evidence
of respiratory distress.
First, you must calculate the alveolar ventilation.
.
VE = 24 x 300 = 7.2 L/min
VD = 24 x 150 = 3.6 L/min
VA = 3.6 L/min. Then
300 ml/min x .863
PaCO2 = ----------------------3.6 L/min
PaCO2 = 71.9 mm Hg
PaCO2 and Alveolar Ventilation: Test Your
Understanding
2. What is the PaCO2 of a patient with respiratory rate 10/min,
tidal volume 600 ml, dead space volume 150 ml, CO2
production 200 ml/min? The patient shows some evidence
of respiratory distress.
PaCO2 and Alveolar Ventilation: Test Your
Understanding
2. What is the PaCO2 of a patient with respiratory rate 10/min,
tidal volume 600 ml, dead space volume 150 ml, CO2
production 200 ml/min? The patient shows some evidence
of respiratory distress.
VA = VE – VD
= 10(600) - 10(150) = 6 - 1.5 = 4.5 L/min
200 ml/min x .863
PaCO2 = ---------------------- = 38.4 mm Hg
4.5 L/min
PaCO2 and Alveolar Ventilation:
Test Your Understanding
3. A man with severe chronic obstructive pulmonary disease exercises on a treadmill at 3
miles/hr. His rate of CO2 production increases by 50% but he is unable to augment
alveolar ventilation. If his resting PaCO2 is 40 mm Hg and resting VCO2 is 200
ml/min, what will be his exercise PaCO2?
PaCO2 and Alveolar Ventilation:
Test Your Understanding
3. A man with severe chronic obstructive pulmonary disease exercises on a treadmill at 3
miles/hr. His rate of CO2 production increases by 50% but he is unable to augment
alveolar ventilation. If his resting PaCO2 is 40 mm Hg and resting VCO2 is 200
ml/min, what will be his exercise PaCO2?
Exercise increases metabolic CO2 production. People with a normal respiratory system are
always able to augment alveolar ventilation to meet or exceed the amount of VA necessary
to excrete any increase in CO2 production. As in this example, patients with severe COPD
or other forms of chronic lung disease may not be able to increase their alveolar ventilation,
resulting in an increase in PaCO2. This patient’s resting alveolar ventilation is
PaCO2 =
VCO2 x .863
--------------VA
200 ml/min x .863
VA = 4.32 L/min = ----------------------40 mm Hg
Since CO2 production increased by 50% and alveolar ventilation not at all, his
exercise PaCO2 is
300 ml/min x .863
-------------------------- = 59.9 mm Hg
4.32 L/min
You can’t learn this material from a
lecture!!
Review:
www.lakesidepress.com/pulmonary/index-phys.html
index to web sites on pulmonary physiology
www.lakesidepress.com/ABGQuiz2009-Questions.htm
multiple-choice blood gas quiz
www.lakesidepress.com/pulmonary/papers/eq/tablecontents.html
4 Most Important Equations in Clinical Practice
www.lakesidepress.com/pulmonary/ABG/MixedAB.htm
Diagnosing mixed acid-base disorders
www.lakesidepress.com/pulmonary/ABG/PO2.htm
PaO2, SaO2 & CaO2 – What’s the Difference?